El objetivo de este trabajo final es utilizar DOS técnicas de las que se vieron durante la materia Estadística Aplicada a la Investigación de Mercado.

1 Aplicaciones de Google Play Store

La base de datos fue extraida de kaggle¹, se trata de un dataset público construido a partir de webscrapping con el objetivo de analizar el mercado de las aplicaciones de android. La misma fue publicada hace 4 años por Lavanya Gupta.

Las variables que posee el dataframe son las siguientes. Es importante resaltar que toda esta información es de cuando fue escrapeada la base. Es decir en 2019.

Variables y descripción
Variable	Descripción
`Apps`	Nombre de la aplicación
`Category`	Categoría a la que pertenece la app
`Rating`	Puntaje que los usuarios le dieron a la app
`Reviews`	Cantidad de comentarios de la app
`Size`	Tamaño de la app
`Installs`	Cantidad de usuarios que descargaron la app
`Type`	Si es paga (paid) o gratuita (free)
`Price`	Precio de la app
`Content Raiting`	Grupo de edad para la cual es la app (Children/Mature +21/ Adult /Everyone)
`Genres`	Genero de la App. Una App puede pertenecer a multiples generos
`Last Updated`	Fecha de la última actualización
`Current Ver`	Versión actual de la aplicación que se encuentra disponible en playstore
`Android Ver`	Versión mínima de android necesaria para descargar la app

La Asociación por el Derecho al Acceso (ADA) quiere desarrollar una aplicación de Google Playstore que sirva para promocionar y difundir el derecho al acceso a la información, por eso necesitan conocer el mercado de aplicaciones de Google Playstore

El objetivo de este trabajo es analizar las características del mercado de las aplicaciones alojadas en Google Play Store para saber cómo influyen las mismas en la popularidad de las aplicaciones (medido por el número de instalaciones). De esta manera, se buscará investigar el mercado de las App para decidir qué variables habría que tener en cuenta para hacer de esta app popular. ¿Debería ser un juego o un aplicativo informativo? ¿Bajo qué rotulo sería conveniente clasificarla?.

En este marco, el trabajo se estructura de la siguiente manera: En primer lugar, se realiza el análisis exploratorio y la limpieza de los datos. En segundo lugar, se exploran cuáles son las características que contribuyen a la popularidad de las aplicaciones. Por último, se tratará de predecir la popularidad de las apps (medido por las instalaciones)

2 Análisis exploratorio y transformación de las variables

Comenzamos por levantar la base de datos y explorar sus variables²:

#Cargamos la base y limpiamos los nombres del dataset 
apps <-  read_csv("Data/googleplaystore.csv") 


bd_apps <- apps %>% 
  clean_names()

#visualizamos los primeros valores
head(bd_apps) %>% 
  gt()

app	category	rating	reviews	size	installs	type	content_rating	genres	last_updated	current_ver	android_ver
Photo Editor & Candy Camera & Grid & ScrapBook	ART_AND_DESIGN	4.1	159	19M	10,000+	Free	Everyone	Art & Design	January 7, 2018	1.0.0	4.0.3 and up
Coloring book moana	ART_AND_DESIGN	3.9	967	14M	500,000+	Free	Everyone	Art & Design;Pretend Play	January 15, 2018	2.0.0	4.0.3 and up
U Launcher Lite – FREE Live Cool Themes, Hide Apps	ART_AND_DESIGN	4.7	87510	8.7M	5,000,000+	Free	Everyone	Art & Design	August 1, 2018	1.2.4	4.0.3 and up
Sketch - Draw & Paint	ART_AND_DESIGN	4.5	215644	25M	50,000,000+	Free	Teen	Art & Design	June 8, 2018	Varies with device	4.2 and up
Pixel Draw - Number Art Coloring Book	ART_AND_DESIGN	4.3	967	2.8M	100,000+	Free	Everyone	Art & Design;Creativity	June 20, 2018	1.1	4.4 and up
Paper flowers instructions	ART_AND_DESIGN	4.4	167	5.6M	50,000+	Free	Everyone	Art & Design	March 26, 2017	1.0	2.3 and up

Composición de las variables:

#visualizamos las variables 
bd_apps %>% 
  skimr::skim()

Data summary
Name	Piped data
Number of rows	10841
Number of columns	13
_______________________
Column type frequency:
character	11
numeric	2
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	n_unique
app	0	1	1	194	9660
category	0	1	3	19	34
size	0	1	3	18	462
installs	0	1	1	14	22
type	0	1	1	4	4
price	0	1	1	8	93
content_rating	1	1	4	15	6
genres	0	1	4	37	120
last_updated	0	1	6	18	1378
current_ver	1	1	1	50	2833
android_ver	1	1	3	18	34

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
rating	1474	0.86	4.19	0.54	1	4	4.3	4.5	19	▇▁▁▁▁
reviews	1	1.00	444152.90	2927760.60	0	38	2094.0	54775.5	78158306	▇▁▁▁▁

# variables por tipo 
bd_apps %>% vis_dat(warn_large_data = F)

#valores perdidos
vis_miss(bd_apps)

#solo hay en rating

Se observa que de 13 columnas, 12 contienen variables de tipo “character” y 2 númericas. A continuación vamos a reconvertir algunas variables.

Rating es la única variable que posee missings en su composición, esto se debe a que en otras variables como size o android version se encuentra el valor “varies with device” que será reemplazado por NA. Además existen valores repetidos. Por lo que nos quedamos sólo con los valores únicos

nrow(bd_apps %>%
  distinct())

## [1] 10358

bd_apps <- bd_apps %>% 
  distinct()

bd_apps %>% 
  filter(installs == "Free") %>% 
  gt()

app	category	rating	reviews	size	installs	type	price	content_rating	genres	last_updated	current_ver	android_ver
Life Made WI-Fi Touchscreen Photo Frame	1.9	19	NA	1,000+	Free	0	Everyone	NA	February 11, 2018	1.0.19	4.0 and up	NA

Eliminamos esta observación dado que tiene un rating que supera los 5 puntos y una categoría que no coincide con la del resto de las apps.

Las variable instalaciones, precio y tamaño poseen caracteres. Vamos a transformarlas para su posterior utilización. Respecto de size la variable contiene “M” (MB) o “K” (KB). Asimismo se observa que existe el valor “varies with device” . Esto es debido a que Google Play permite publicar diferentes APK para cada aplicación. Cada uno dirigido a una configuración de dispositivo diferente. Por lo que, al seleccionar “instalar” el sistema Android selecciona los recursos apropiados para el dispositivo. Para poder convertir esta variable a numérica se pasará todo a KB. Es decir multiplicando los MB * 1000, dado que 1 MB = 1000 KB. Sucede lo mismo con Android versión que posee valores correspondientes a “varies with device”

#pasamos a formato fecha la variable last_updated
bd_apps <- bd_apps %>%
  filter(app != "Life Made WI-Fi Touchscreen Photo Frame") %>% 
  mutate(last_updated = mdy(last_updated),
         installs = gsub("\\+",'',installs), #eliminamos los simbolos 
         installs = gsub(",",'',installs),
         installs = as.numeric(installs),
         reviews = as.numeric(reviews), #pasamos a numérico
         price = as.numeric(gsub("\\$", "", as.character(price))), #eliminamos los simbolos
         android_ver = gsub("Varies with device", NA, android_ver), #varies with device lo pasamos a NA
    android_ver = as.numeric(substr(android_ver, start = 1, stop = 3)),
     size_num = ifelse(grepl("M", size), as.numeric(sub("([0-9\\.]+)M", "\\1", size))*1000, as.numeric(sub("([0-9\\.]+)k", "\\1", size)))) %>% #dejamos un solo decimal 
  filter(type %in% c("Free", "Paid"))
    # Hay dos apps que tienen 0 o NA, vamos a eliminarlas y quedarnos solo con las que tienen Free o PAID en Type
  
bd_apps %>% 
  skimr::skim()

Data summary
Name	Piped data
Number of rows	10356
Number of columns	14
_______________________
Column type frequency:
character	7
Date	1
numeric	6
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	n_unique
app	0	1	1	194	9658
category	0	1	4	19	33
size	0	1	3	18	461
type	0	1	4	4	2
content_rating	0	1	4	15	6
genres	0	1	4	37	119
current_ver	1	1	1	50	2832

Variable type: Date

skim_variable	n_missing	complete_rate	min	max	median	n_unique
last_updated	0	1	2010-05-21	2018-08-08	2018-05-20	1377

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
rating	1464	0.86	4.19	0.52	1.0	4	4.3	4.50	5	▁▁▁▆▇
reviews	0	1.00	405943.81	2696905.10	0.0	32	1683.0	46438.25	78158306	▇▁▁▁▁
installs	0	1.00	14159126.55	80243307.58	0.0	1000	100000.0	1000000.00	1000000000	▇▁▁▁▁
price	0	1.00	1.03	16.28	0.0	0	0.0	0.00	400	▇▁▁▁▁
android_ver	1222	0.88	3.85	0.84	1.0	4	4.1	4.10	8	▂▁▇▁▁
size_num	1525	0.85	21287.79	22540.25	8.5	4700	13000.0	29000.00	100000	▇▂▁▁▁

2.0.0.1 Type

#transformamos type a binaria
bd_apps$type_bin <- ifelse(bd_apps$type == "Paid", 1, 0)

#mostramos el resultado
g2 <- bd_apps %>% 
  group_by(type) %>% 
  summarise(N=n()) %>% 
  ggplot(aes(N, reorder(type,N))) +
  geom_col(fill = "#009999") +
  theme_classic() +
  labs(x = " ",
       y = " ",
       title = "Distribución de aplicaciones por tipo (pago/gratuito") 


ggplotly(g2)

La variable type muestra si la aplicación es paga o gratuita, para poder utilizarla en los análisis la transformaremos en una variable binaria asignandole 1 si es paga y 0 si es gratuita

2.0.0.2 Content raiting

Vamos a modificar esta variable para generar rangos de edad

bd_apps <- bd_apps %>%
  mutate(grupo_edades =  case_when(content_rating == "Everyone" ~ "4+",
                                     content_rating == "Everyone 10+" ~ "9+",
                                     content_rating == "Teen" ~ "12+",
                                     content_rating == "Mature 17+" ~ "17+",
                                     content_rating == "Unrated" ~ "9+",
                                   content_rating == "Adults only 18+" ~ "17+"))

bd_apps %>% 
  filter(content_rating == "Unrated") %>% 
  gt()

app	category	rating	reviews	size	installs	type	price	content_rating	genres	last_updated	current_ver	android_ver	size_num	type_bin	grupo_edades
Best CG Photography	FAMILY	NaN	1	2.5M	500	Free	0	Unrated	Entertainment	2015-06-24	5.2	3.0	2500	0	9+
DC Universe Online Map	TOOLS	4.1	1186	6.4M	50000	Free	0	Unrated	Tools	2012-02-27	1.3	2.3	6400	0	9+

g1 <- bd_apps %>% 
  group_by(grupo_edades) %>% 
  summarise(N=n()) %>% 
  ggplot(aes(N, reorder(grupo_edades,N))) +
  geom_col(fill = "#009999") +
  theme_classic() +
  labs(x = "Número de aplicaciones",
       y = "Grupo de edades",
       title = "Distribución de aplicaciones por grupo de edades") 


ggplotly(g1)

Hay dos apps sin calificar que son Best CG Photography y DC Universe Online Map. como son herramientas, vamos a clasificarlas como “Everyone” osea +9. Hay solo 3 aplicaciones que corresponden a +18, se las incorporará a +17.

#vemos la distribución de los grupos de edad en las apps
edades <- bd_apps %>%
    group_by(grupo_edades) %>%
    summarize(Total = n()) %>%
    mutate(perc = round(Total/sum(Total) * 100)) %>%
    arrange(-perc)

perc_counts <- edades$perc
names(perc_counts) <- edades$grupo_edades

# Graficamos

waffle(perc_counts) + 
  theme_minimal() +
  theme(axis.text.y = element_blank(),
        axis.ticks.y = element_blank(),
        axis.text.x = element_blank(),
        plot.title = element_text(hjust = 0.5)) +
  labs(title = "Porcentaje de apps por grupos de edad")

rm(edades)
rm(perc_counts)

La mayoría de las aplicaciones está catalogada como “Everyone” o apta para mayores de 4 años.

2.0.0.3 genres

bd_apps %>%
  group_by(genres) %>%
  summarise(n = n()) %>% 
  head(15) %>% 
  gt()

genres	n
Action	356
Action;Action & Adventure	15
Adventure	75
Adventure;Action & Adventure	13
Adventure;Brain Games	1
Adventure;Education	2
Arcade	218
Arcade;Action & Adventure	15
Arcade;Pretend Play	1
Art & Design	58
Art & Design;Action & Adventure	2
Art & Design;Creativity	7
Art & Design;Pretend Play	2
Auto & Vehicles	85
Beauty	53

#exploramos las etiquetas, dividimos las etiquetas 

generos <- bd_apps %>%
  separate_rows(genres, sep = ";") %>% 
 # separate_rows(genres, sep = "&") %>% 
  count(genres) %>% 
  arrange(desc(n))

g3 <- ggplot(generos, aes(x = genres, y = n)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  xlab("Género") +
  ylab("Frecuencia") +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(x = "Géneros",
       y = "N° de apps",
       title = "Distribución de aplicaciones por género") 


ggplotly(g3)

La variable genres contiene etiquetas que definen el género de la aplicación. Es decir una app puede tener más de una etiqueta. Debido a la cantidad de categorías que posee la variable se decide eliminarla para el desarrollo de los posteriores modelos

2.0.1 Valores Nulos

# Valores nulos

md.pattern(bd_apps, rotate.names = TRUE, plot = TRUE)

##      app category reviews size installs type price content_rating genres
## 7368   1        1       1    1        1    1     1              1      1
## 343    1        1       1    1        1    1     1              1      1
## 1407   1        1       1    1        1    1     1              1      1
## 15     1        1       1    1        1    1     1              1      1
## 55     1        1       1    1        1    1     1              1      1
## 1125   1        1       1    1        1    1     1              1      1
## 42     1        1       1    1        1    1     1              1      1
## 1      1        1       1    1        1    1     1              1      1
##        0        0       0    0        0    0     0              0      0
##      last_updated type_bin grupo_edades current_ver android_ver rating size_num
## 7368            1        1            1           1           1      1        1
## 343             1        1            1           1           1      1        0
## 1407            1        1            1           1           1      0        1
## 15              1        1            1           1           1      0        0
## 55              1        1            1           1           0      1        1
## 1125            1        1            1           1           0      1        0
## 42              1        1            1           1           0      0        0
## 1               1        1            1           0           1      1        1
##                 0        0            0           1        1222   1464     1525
##          
## 7368    0
## 343     1
## 1407    1
## 15      2
## 55      1
## 1125    2
## 42      3
## 1       1
##      4212

# Visualización de perdidos
gg_miss_var(bd_apps, show_pct = T)

#Analizamos el patrón de los valores nulos
gg_miss_upset(bd_apps,nsets = 10)

Se observa que hay un patrón en los datos faltantes de android_ver , rating y size_num por lo que no es posible eliminar los valores nulos.

2.0.1.1 Rating

Más arriba se observó que la variable rating tiene valores nulos. Observamos la distribución de estos valores en relación a la cantidad de descargas

t2 <- bd_apps %>% 
  filter(is.na(rating)) %>% 
  count(reviews) %>% 
  mutate(porcentaje = round(n/1474*100, 2),
         porcentaje_acumulado = cumsum(porcentaje)) 


#analizamos los ratings por cantidad de reviews

t1 <- bd_apps %>% 
  filter(is.na(rating)) %>% 
  count(installs) %>% 
  mutate(porcentaje = round(n/1474*100, 2),
         porcentaje_acumulado = cumsum(porcentaje)) 

kable(list(t1, t2))

installs	n	porcentaje	porcentaje_acumulado
0	14	0.95	0.95
1	64	4.34	5.29
5	73	4.95	10.24
10	316	21.44	31.68
50	148	10.04	41.72
100	407	27.61	69.33
500	129	8.75	78.08
1000	192	13.03	91.11
5000	43	2.92	94.03
10000	44	2.99	97.02
50000	12	0.81	97.83
100000	19	1.29	99.12
500000	1	0.07	99.19
1000000	2	0.14	99.33

reviews	n	porcentaje	porcentaje_acumulado
0	592	40.16	40.16
1	205	13.91	54.07
2	131	8.89	62.96
3	94	6.38	69.34
4	63	4.27	73.61
5	34	2.31	75.92
6	34	2.31	78.23
7	26	1.76	79.99
8	17	1.15	81.14
9	26	1.76	82.90
10	18	1.22	84.12
11	13	0.88	85.00
12	7	0.47	85.47
13	12	0.81	86.28
14	11	0.75	87.03
15	5	0.34	87.37
16	4	0.27	87.64
17	12	0.81	88.45
18	2	0.14	88.59
19	8	0.54	89.13
20	7	0.47	89.60
21	6	0.41	90.01
22	3	0.20	90.21
23	5	0.34	90.55
24	9	0.61	91.16
25	3	0.20	91.36
26	2	0.14	91.50
27	2	0.14	91.64
28	2	0.14	91.78
29	1	0.07	91.85
30	8	0.54	92.39
31	7	0.47	92.86
32	1	0.07	92.93
34	2	0.14	93.07
35	3	0.20	93.27
36	1	0.07	93.34
37	3	0.20	93.54
38	6	0.41	93.95
40	4	0.27	94.22
41	2	0.14	94.36
44	2	0.14	94.50
45	2	0.14	94.64
46	1	0.07	94.71
49	3	0.20	94.91
51	1	0.07	94.98
53	1	0.07	95.05
54	2	0.14	95.19
55	2	0.14	95.33
57	1	0.07	95.40
59	1	0.07	95.47
61	2	0.14	95.61
62	1	0.07	95.68
63	1	0.07	95.75
64	1	0.07	95.82
65	1	0.07	95.89
67	2	0.14	96.03
68	1	0.07	96.10
72	1	0.07	96.17
76	2	0.14	96.31
77	1	0.07	96.38
82	1	0.07	96.45
83	1	0.07	96.52
86	1	0.07	96.59
88	2	0.14	96.73
91	1	0.07	96.80
94	1	0.07	96.87
95	2	0.14	97.01
96	2	0.14	97.15
102	1	0.07	97.22
104	1	0.07	97.29
110	1	0.07	97.36
114	2	0.14	97.50
119	1	0.07	97.57
130	1	0.07	97.64
142	1	0.07	97.71
145	1	0.07	97.78
154	1	0.07	97.85
160	1	0.07	97.92
161	1	0.07	97.99
163	1	0.07	98.06
174	1	0.07	98.13
182	1	0.07	98.20
196	1	0.07	98.27
221	1	0.07	98.34
235	1	0.07	98.41
239	1	0.07	98.48
250	1	0.07	98.55
350	1	0.07	98.62
363	1	0.07	98.69
414	1	0.07	98.76
487	1	0.07	98.83
649	1	0.07	98.90
654	1	0.07	98.97
776	1	0.07	99.04
970	1	0.07	99.11
1317	1	0.07	99.18
1330	1	0.07	99.25
2221	1	0.07	99.32
2536	1	0.07	99.39
3248	1	0.07	99.46

El 80% de las aplicaciones que poseen missings en la variable rating tienen menos de 500 descargas y menos de 10 reviews. Esto se puede deber a que como fueron poco descargadas todavía la gente no las ha puntuado o algún error en el webscrapping.

2.0.1.2 Tamaño (size)

bd_apps %>% 
  group_by(size_num) %>% 
  summarise(N= n()) %>% 
  arrange(desc(N)) %>% 
  head() %>% 
  gt()

size_num	N
NA	1525
11000	188
12000	186
13000	186
14000	182
15000	174

De 10356 registros 1525 (15%) no poseen un tamaño definido por lo expresado más arriba. Vamos a ver la distribución de esta variable:

# histograma de la variable "size"
p1<- ggplot(bd_apps, aes(x = size_num)) + 
  geom_histogram(color="black", fill="lightblue", binwidth = 5000) +
  labs(title = "Distribución del tamaño de las aplicaciones",
       x = "Tamaño (KB)", y = "Frecuencia") +
  theme_minimal() +
  theme(plot.title = element_text(size=14, face="bold"),
        axis.title.x = element_text(size=12),
        axis.title.y = element_text(size=12),
        axis.text = element_text(size=10))

# densidad de la variable "size"
p2 <-ggplot(bd_apps, aes(x = size_num)) + 
  geom_density(color="black", fill="lightblue") +
  labs(x = "Tamaño (KB)", y = "Densidad") +
  theme_minimal() +
  theme(plot.title = element_text(size=14, face="bold"),
        axis.title.x = element_text(size=12),
        axis.title.y = element_text(size=12),
        axis.text = element_text(size=10))

grid.arrange(p1, p2, ncol=2)

2.0.1.3 Android version

Hay 1352 filas que contienen NA porque corresponde a la categoría “varies with devices”.

bd_apps %>%
  group_by(android_ver) %>%
  summarise(n = n()) %>%
  ggplot(aes(x = as.factor(android_ver), y = n, fill = android_ver)) +
  geom_bar(stat = "identity") +
  labs(x = "Versión de Android", y = "Frecuencia", fill = "Versión de Android") +
  theme_classic()

2.0.1.4 current_ver

bd_apps %>%
  group_by(current_ver) %>%
  summarise(n = n()) %>% 
  arrange(desc(n)) %>% 
  head() %>% 
  gt()

current_ver	n
Varies with device	1301
1.0	802
1.1	260
1.2	177
2.0	149
1.3	142

La variable current_ver tiene 2833 valores únicos, el 25% de los registros. Esto sugiere que no es muy informativa. Además, no puede ser convertida a numérica ya que es una variable categorica que indica la versión actual de la aplicación. No siempre el número de versión es un número continuo. Por este motivo se decide prescindir de esta variable para el posterior análisis

A continuación utilizaremos la técnica de imputación múltiple del paquete ´mice´ para los valores nulos

#Imputamos los NA

imp <- mice(bd_apps[, c("size_num", "rating", "android_ver")])

# Visualizamos la distribución de variables antes y después de la imputación
kableExtra::kable(summary(bd_apps[, c("size_num", "rating", "android_ver")]),caption = "Extructura variables previo a imputar")

Extructura variables previo a imputar
size_num	rating	android_ver
Min. : 8.5	Min. :1.000	Min. :1.000
1st Qu.: 4700.0	1st Qu.:4.000	1st Qu.:4.000
Median : 13000.0	Median :4.300	Median :4.100
Mean : 21287.8	Mean :4.188	Mean :3.853
3rd Qu.: 29000.0	3rd Qu.:4.500	3rd Qu.:4.100
Max. :100000.0	Max. :5.000	Max. :8.000
NA’s :1525	NA’s :1464	NA’s :1222

kableExtra::kable(summary(complete(imp)[, c("size_num", "rating", "android_ver")]),caption = "Extructura variables imputadas")

Extructura variables imputadas
size_num	rating	android_ver
Min. : 8.5	Min. :1.000	Min. :1.000
1st Qu.: 4800.0	1st Qu.:4.000	1st Qu.:4.000
Median : 13000.0	Median :4.300	Median :4.100
Mean : 21648.0	Mean :4.185	Mean :3.857
3rd Qu.: 30000.0	3rd Qu.:4.500	3rd Qu.:4.100
Max. :100000.0	Max. :5.000	Max. :8.000

# Agregamos las variables originales a la base imputada
bd_apps_imputed <- cbind(bd_apps[, setdiff(colnames(bd_apps), colnames(imp))], complete(imp))

# Renombrar las columnas imputadas
colnames(bd_apps_imputed)[17:19] <- paste0(colnames(bd_apps_imputed)[17:19], "_imp")

#sacamos las variables que no nos sirven o las ya imputadas y creamos la base que se va a utilizar para el desarrollo de la consigna
df_apps <- bd_apps_imputed %>% 
  select(-rating,
         -size,
         -size_num,
         -android_ver,
         -content_rating,
         -current_ver)

# Verificamos la estructura de la nueva base de datos
skimr::skim(df_apps)

Data summary
Name	df_apps
Number of rows	10356
Number of columns	13
_______________________
Column type frequency:
character	5
Date	1
numeric	7
________________________
Group variables	None

Variable type: character

skim_variable	complete_rate	min	max	n_unique
app	1	1	194	9658
category	1	4	19	33
type	1	4	4	2
genres	1	4	37	119
grupo_edades	1	2	3	4

Variable type: Date

skim_variable	n_missing	complete_rate	min	max	median	n_unique
last_updated	0	1	2010-05-21	2018-08-08	2018-05-20	1377

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
reviews	1	405943.81	2696905.10	0.0	32	1683.0	46438.25	78158306	▇▁▁▁▁
installs	1	14159126.55	80243307.58	0.0	1000	100000.0	1000000.00	1000000000	▇▁▁▁▁
price	1	1.03	16.28	0.0	0	0.0	0.00	400	▇▁▁▁▁
type_bin	1	0.07	0.26	0.0	0	0.0	0.00	1	▇▁▁▁▁
size_num_imp	1	21647.96	22755.34	8.5	4800	13000.0	30000.00	100000	▇▂▁▁▁
rating_imp	1	4.19	0.53	1.0	4	4.3	4.50	5	▁▁▁▆▇
android_ver_imp	1	3.86	0.84	1.0	4	4.1	4.10	8	▂▁▇▁▁

Volvemos a ver cómo quedó la estructura de los valores nulos

# variables por tipo 
df_apps %>% vis_dat(warn_large_data = F)

#valores perdidos
vis_miss(df_apps)

2.0.2 Valores Atípicos

A continuación boxplot.stats calcula el límite inferior y superior de cada variable, y luego suma los valores que se encuentran por debajo y por encima del limite superior

count_outliers <- function(x) {
  bp <- boxplot.stats(x)
  sum(x < bp$stats[1] | x > bp$stats[5])
}

bd_numerico <- df_apps %>% 
  select_if(is.numeric)



# Contamos los outliers en la base de datos de ejemplo
sapply(bd_numerico, count_outliers)

##         reviews        installs           price        type_bin    size_num_imp 
##            1869            2566             765             765             636 
##      rating_imp android_ver_imp 
##             586            4034

# Boxplots

plot1 <- ggplot(df_apps, aes(y = installs)) + 
  geom_boxplot(aes(fill = "installs")) +
  scale_fill_manual(values = '#FF689f', guide= FALSE) +
  ggtitle("Boxplot para la variable installs") +
  ylab("Cantidad") +
  theme_classic()

plot2 <- ggplot(df_apps, aes(y = price)) + 
  geom_boxplot(aes(fill = "price")) +
  scale_fill_manual(values = '#DC71FA', guide= FALSE) +
  ggtitle("Boxplot para la variable price") +
  ylab("Cantidad") +
  theme_classic()

plot3 <- ggplot(df_apps, aes(y = rating_imp )) + 
  geom_boxplot(aes(fill = "rating_imp")) +
  scale_fill_manual(values = '#00ABFD', guide= FALSE) +
  ylab("Cantidad") +
  theme_classic() + 
  ggtitle("Boxplot para la variable raiting")

# Boxplot de type_bin
plot4 <- ggplot(df_apps, aes(x = "", y = reviews)) +
  geom_boxplot(aes(fill = "reviews")) +
  scale_fill_manual(values = '#00C1AA', guide= FALSE)+
  ggtitle("Boxplot de type_bin")+
  ylab("Cantidad") +
  theme_classic()

plot5 <- ggplot(df_apps, aes(y = size_num_imp)) + 
  geom_boxplot(aes(fill = "size_num_imp")) +
  scale_fill_manual(values = '#39B600', guide= FALSE)+
  ggtitle("Boxplot para la variable size_num") +
  ylab("Tamaño en MB") +
  theme_classic()


plot6 <-ggplot(df_apps, aes(y = android_ver_imp  )) + 
  geom_boxplot(aes(fill = "android_ver_imp")) +
  scale_fill_manual(values = '#F37B59', guide= FALSE)+
  ggtitle("Boxplot para la variable android version") +
  ylab("Cantidad") +
  theme_classic()

grid.arrange(plot1, plot2, plot3, plot4, plot5, plot6, ncol = 2)

Se observa presencia de outliers en la mayoría de las variables numéricas. Esto se debe a la dispersión de los datos y no a un error en la medición. Es decir, hay aplicaciones con mayor precio o cantidad de instalaciones que otras. El caso de typebin es porque es una variable binaria por lo que no conviene imputar los outliers para no generar cambios en su distribución.

En la variable price existen valores atípicos porque gran parte de la muestra de apps es gratuita. En este caso se decide no imputar esos valores, ya que son legítimos y representan el precio real de las aplicaciones.

quantile(df_apps$price, na.rm=TRUE)

##   0%  25%  50%  75% 100% 
##    0    0    0    0  400

El 75% de las apps son gratuitas. Para los análisis posteriores se decidió omitir esta variable. Se utilizará solo type, es decir si la aplicación es paga o gratuita

df_apps <- df_apps %>% 
  select(-price)

Reviews

ggplot(df_apps, aes(x = reviews)) +
  geom_histogram(bins = 30, color = "black", fill = "lightblue") + 
  labs(title = "Histograma de Reviews", x = "Número de Reviews", y = "Frecuencia")

summary(df_apps$reviews)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##        0       32     1683   405944    46438 78158306

Se puede ver que la mayoría de las apps tienen pocas reviews. El 50% tiene 1683 o menos. Por lo que se observa que hay algunos outliers. También se puede observar que hay una gran variabilidad en la cantidad de reseñas, con una media de 405944 y un valor máximo de 78158306, lo que sugiere la presencia de outliers

Reemplazar los outliers de variables como rating y android_ver no la consideramos apropiada debido a que, la primera solo tiene valores del 1 al 5; y, la segunda del 1 al 8.

plot1 <- ggplot(df_apps, aes(x = rating_imp)) +
  geom_histogram(binwidth = 0.5, fill = "#00ABFD", color = "white") +
  ggtitle("Distribución de Rating") +
  xlab("Rating") +
  ylab("Frecuencia") +
  theme_classic()

plot_3 <- ggplot(df_apps, aes(x = rating_imp)) +
  geom_density(fill = "#00ABFD", color = "white") +
  ggtitle("Densidad de rating") +
  xlab("Rating") +
  ylab("Densidad") +
  theme_classic()


plot2 <- ggplot(df_apps, aes(x = android_ver_imp)) +
  geom_histogram(binwidth = 0.5, fill = "#00ABFD", color = "white") +
  ggtitle("Distribución de android_ver") +
  xlab("version android") +
  ylab("Frecuencia") +
  theme_classic()

plot4 <- ggplot(df_apps, aes(x = android_ver_imp)) +
  geom_density(fill = "#00ABFD", color = "white") +
  ggtitle("Densidad de android_ver") +
  xlab("versión android") +
  ylab("Densidad") +
  theme_classic()

grid.arrange(plot1, plot_3, plot2,plot4, ncol =2 )

A continuación se imputarán los valores atípicos para las variables installs, reviews y size a través de winzonrize del paquete robustHD para reducir el impacto de los valores extremos o atípicos. Esta técnica se utiliza para reemplazar los outliers por los valores mas cercanos.

#imputamos los outliers

df_final <- df_apps %>%
  mutate(installs = winsorize(installs, probs = c(0.05, 0.95)),
         reviews = winsorize(reviews, probs = c(0.05, 0.95)),
         size_num_imp = winsorize(size_num_imp, probs = c(0.05, 0.95)))

Analizamos la nueva distribución:

bd_numerico2 <- df_final %>% 
  select_if(is.numeric)

# Contar los outliers en la base de datos de ejemplo
sapply(bd_numerico2, count_outliers)

##         reviews        installs        type_bin    size_num_imp      rating_imp 
##               0               0             765               0             586 
## android_ver_imp 
##            4034

# Crear el boxplot
plot1 <- ggplot(df_final, aes(y = installs)) + 
  geom_boxplot(aes(fill = "installs")) +
  scale_fill_manual(values = '#FF689f', guide= FALSE) +
  ggtitle("Boxplot para la variable installs") +
  ylab("Cantidad") +
  theme_classic()


plot5 <- ggplot(df_final, aes(y = size_num_imp)) + 
  geom_boxplot(aes(fill = "size_num_imp")) +
  scale_fill_manual(values = '#39B600', guide= FALSE)+
  ggtitle("Boxplot para la variable size_num") +
  ylab("Tamaño en MB") +
  theme_classic()

plot6 <-ggplot(df_final, aes(y = reviews  )) + 
  geom_boxplot(aes(fill = "reviews")) +
  scale_fill_manual(values = '#F37B59', guide= FALSE)+
  ggtitle("Boxplot para la variable android version") +
  ylab("Cantidad") +
  theme_classic()

grid.arrange(plot1,plot5, plot6, ncol = 1)

2.0.3 Popularidad ~ Instalaciones

2.0.3.1 Categorías

g <- df_final %>% 
  group_by(category) %>% 
  summarise(N = n()) %>% 
  ggplot(aes(x = category, y = N, size = N, color = category)) +
  geom_point() +
  theme_classic()+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  labs(x = "", y = " ", title = "Cantidad de apps por categoría") +
  theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold")) +
  theme(legend.position = "none") 



ggplotly(g)

rm(g)

Se puede observar que de las categorías existentes la mayoría de las apps se encuentran clasificadas como Family, Game y Tools. A continuación se analizan cuales son las categorías más instaladas:

g <- df_final %>% 
  group_by(category) %>% 
  summarise(descargas = sum(installs)) %>% 
  ggplot(aes(x = reorder(category,-descargas), y = descargas, size = descargas, color = category)) +
  geom_point() +
  theme_classic()+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  labs(x = "", y = " ", title = "Categorías más populares (Cantidad de instalaciones)", caption = "En millones de descargas") +
  theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold")) +
  theme(legend.position = "none") +
  scale_y_continuous(labels = scales::comma)

# bd_apps %>% 
#   group_by(category) %>% 
#   summarise(descargas = sum(installs)) %>% 
#   arrange(desc(descargas))

ggplotly(g)

rm(g)

Se puede observar que las categorías más populares son GAME y FAMILY

2.0.3.2 Tipo de app (gratuita o paga)

g4 <- ggplot(df_final, aes(x=type, y=installs, fill=type)) +
  geom_boxplot() +
  scale_fill_brewer(palette = "Set2") +
  scale_y_continuous(labels = scales::comma) +
  theme_classic() +
  ggtitle(label = "Boxplot instalaciones por tipo") +
  guides(fill=FALSE)

ggplotly(g4)

rm(g4)

Las aplicaciones gratuitas son mas instaladas en general

2.0.3.3 Grupo de edades

# Convertir a gráfico interactivo
p <- ggplot(df_final, aes(x = reorder(grupo_edades,installs), y = installs)) +
  geom_bar(stat = "identity", fill = "#FB8072") +
  labs(title = "Cantidad de instalaciones por grupos de edades",
       x = "Grupos de Edades", y = "Cantidad de instalaciones") +
  theme_classic() 

ggplotly(p)

rm(p)

Se puede observar que las apps más descargadas son las habilitadas para +4 años (toda la familia)

2.0.3.4 Rating

p <- df_final %>% 
  mutate(rating_imp = round(rating_imp,0)) %>% 
  ggplot(aes(x = reorder(rating_imp,installs), y = installs)) +
  geom_bar(stat = "identity", fill = "#FB8072") +
  labs(title = "Cantidad de instalaciones por rating",
       x = "Rating", y = "Cantidad de instalaciones") +
  theme_classic() 

ggplotly(p)

rm(p)

Las apps con mayor cantidad de instalaciones son las que tienen un puntaje de 4 estrellas.

2.0.3.5 tamaño

ggplot(df_final, aes(x = installs, y = size_num_imp, fill = size_num_imp)) +
  geom_boxplot(fill = "#FB8072") + theme_classic()  +
  scale_y_continuous(labels = scales::comma) +
  ylab("Instalaciones") +
  xlab("Tamaño") +
  ggtitle("Relación entre tamaño y cantidad de instalaciones")

Las apps con mayor cantidad de instalaciones se encuentran entre 10000 y 30000 KB

2.0.3.6 Actualización

plot1 <- df_final %>%
  group_by(last_updated) %>%
  summarise(total_installs = sum(installs)) %>%
  ggplot(aes(x = last_updated, y = total_installs)) +
  geom_line(color = "#FF689f", size = 1) +
  labs(x = "Fecha de actualización", y = "Instalaciones", 
       title = "Total de instalaciones por fecha de actualización") +
  theme_classic() +
  theme(plot.title = element_text(size = 14, face = "bold"),
        axis.text.x = element_text(angle = 90, vjust = 0.5, size = 10),
        axis.text.y = element_text(size = 10),
        axis.title = element_text(size = 12, face = "bold"),
        legend.title = element_blank(),
        legend.position = "none")

ggplotly(plot1)

Se puede observar que las aplicaciones más populares son las que poseen actualización más reciente (2018). Por lo que, para incluirla en los analisis convertimos la variable a año. Armamos una variable que sea “Año de actualización” para poder incluirla en los análisis posteriores

df_final <- df_final %>% 
  mutate(ano_act = year(last_updated))

#observamos la distribución por año
df_final %>% 
  group_by(ano_act) %>% 
  summarise(N=n()) %>% 
  gt()

ano_act	N
2010	1
2011	15
2012	26
2013	108
2014	204
2015	454
2016	789
2017	1826
2018	6933

3 Análisis de la popularidad de las Apps de Google Play Store

3.0.1 Árbol de decisión ³

El árbol de decisión es un modelo de aprendizaje automático que divide los datos en subconjuntos más pequeños basados en diferentes características y reglas. El objetivo es encontrar las variables que tienen la mayor influencia en la popularidad (medido por la cantidad de instalaciones) de una aplicación, para así encarar el desarrollo de la aplicación que contribuya a difundir el derecho de acceso de la mejor manera. De esta manera, se buscará identificar las variables más importantes para explicar la variabilidad de la variable objetivo.

Analizamos la correlación entre las variables numéricas:

#Guardamos el CSV
write.csv(df_final, "df_final.csv")

#armamos una matriz de correlación 
matriz_df <- df_final %>% 
  select_if(is.numeric)

matriz_df <- cor(matriz_df)
matriz_df

##                     reviews    installs    type_bin size_num_imp rating_imp
## reviews          1.00000000  0.93540955 -0.16366458   0.30863061 0.18104029
## installs         0.93540955  1.00000000 -0.23489469   0.28906019 0.12983148
## type_bin        -0.16366458 -0.23489469  1.00000000  -0.02798766 0.02957440
## size_num_imp     0.30863061  0.28906019 -0.02798766   1.00000000 0.06648153
## rating_imp       0.18104029  0.12983148  0.02957440   0.06648153 1.00000000
## android_ver_imp  0.05965945  0.06238828 -0.10790581   0.17620397 0.05616275
## ano_act          0.22045246  0.22614106 -0.17713161   0.22549474 0.12548035
##                 android_ver_imp    ano_act
## reviews              0.05965945  0.2204525
## installs             0.06238828  0.2261411
## type_bin            -0.10790581 -0.1771316
## size_num_imp         0.17620397  0.2254947
## rating_imp           0.05616275  0.1254804
## android_ver_imp      1.00000000  0.4859452
## ano_act              0.48594524  1.0000000

c1 <- matriz_df %>% 
  ggcorrplot:::ggcorrplot(type = "lower",  lab=TRUE, hc.order = TRUE, title = "Matriz de correlación R", colors = c("#6D9EC1", "white", "purple")) +
  theme(text = element_text(size = 10),
        axis.text.x =  element_text(angle=90, hjust=1, size = 7),
        axis.text.y =  element_text(size = 7))

ggplotly(c1)

#Borramos los datasets para optimizar memoria
rm(c1)
rm(matriz_df)

La variable con más correlación positiva es reviews

3.0.1.1 Preparación y estandarización de las variables

Creamos una variable llamada popular con la variable installs para luego comparar con qué variable el modelo predice mejor.

#Borramos los datasets para optimizar memoria
rm(plot1)
rm(count_outliers)
rm(fa_apps)

#convertimos a factor las variables categóricas



### Distribución de la variable installs
df_final %>% 
  group_by(installs) %>% 
  summarise(N=n()) %>% 
  gt() %>% 
  tab_header(title = "Apps por cantidad de instalaciones")

installs	N
Apps por cantidad de instalaciones
0.0	14
1.0	67
5.0	82
10.0	385
50.0	204
100.0	710
500.0	328
1000.0	890
5000.0	469
10000.0	1033
50000.0	474
100000.0	1129
396371.7	517
396371.7	4054

#Creo variables dummys y estandarizo las variables
df_accesin <- df_final %>% 
  mutate(category = as.factor(category),
         grupo_edades = as.factor(grupo_edades),
         ano_act = as.factor(ano_act),
         popular = ifelse(installs >= 100000, 1,0)) %>%
  select(-last_updated, -type, -genres)%>%  
  recipes::step_scale(all_numeric(), except = c("type_bin","popular", "installs")) %>% 
  select(-steps)


#df_accesin %>% group_by(android_ver_imp) %>% summarise(N=n())
#ponemos el nombre de la app como nombre de la fila 
df_accesin$app <- paste0(seq_len(nrow(df_accesin)), "_", df_accesin$app)
rownames(df_accesin) <- df_accesin$app


df_accesin_cat <- df_accesin %>% 
  select_if(is.factor) 

#Creating Dummy Variables
dummy<- data.frame(sapply(df_accesin_cat,function(x) data.frame(model.matrix(~x-1,data =df_accesin_cat))[,-1]))

dummy %>% 
  head(10) %>% 
  gt()

grupo_edades.x4.	ano_act.x2017	ano_act.x2018
1	0	1
1	0	1
1	0	1
0	0	1
1	0	1
1	1	0
1	0	1
1	0	1
1	1	0
1	0	1

df_accesin_int <- df_accesin %>% 
  select_if(is.numeric) 

df_analisis <- cbind(df_accesin_int,dummy)

##Creamos un dataset con la variable popular y otro con la variable installs
df_popular <- df_analisis %>% 
  select(-installs)

accesin_final <- df_analisis %>% 
  select(-popular)

Observamos la matriz de correlación con las variables binarias

matriz_df <- accesin_final %>% 
  select_if(is.numeric)

matriz_df <- cor(matriz_df)

c1 <- matriz_df %>% 
  ggcorrplot:::ggcorrplot(type = "full",  lab=FALSE, hc.order = FALSE, colors = c("#6D9EC1", "white", "purple"), ggtheme = ggplot2::theme_classic) +
  ggtitle("Matriz de correlación R") +
  theme(text = element_text(size = 5),
        axis.text.x =  element_text(angle=90, hjust=1, size = 5),
        axis.text.y =  element_text(size = 5))

ggplotly(c1)

Las variables con mayor correlación son

# Seleccionar las columnas que tienen una correlación mayor a 0.5
  
cols_sel <- matriz_df %>%
  abs() %>%
  as.data.frame() %>%
  rownames_to_column(var = "var1") %>%
  pivot_longer(cols = -var1, names_to = "var2", values_to = "cor") %>%
  filter(var1 != var2 & cor > 0.3) %>% 
  arrange(desc(cor))

cols_sel %>% 
  gt() %>% 
  tab_header(title = "Variables con mayor correlación")

var1	var2	cor
Variables con mayor correlación
reviews	installs	0.9354096
installs	reviews	0.9354096
ano_act.x2017	ano_act.x2018	0.6584655
ano_act.x2018	ano_act.x2017	0.6584655
category.xDATING	grupo_edades.x17.	0.5543406
grupo_edades.x17.	category.xDATING	0.5543406
grupo_edades.x17.	grupo_edades.x4.	0.4391950
grupo_edades.x4.	grupo_edades.x17.	0.4391950
ano_act.x2016	ano_act.x2018	0.4087029
ano_act.x2018	ano_act.x2016	0.4087029
grupo_edades.x4.	grupo_edades.x9.	0.4010739
grupo_edades.x9.	grupo_edades.x4.	0.4010739
android_ver_imp	ano_act.x2018	0.3965828
ano_act.x2018	android_ver_imp	0.3965828
reviews	size_num_imp	0.3086306
size_num_imp	reviews	0.3086306
ano_act.x2015	ano_act.x2018	0.3047359
ano_act.x2018	ano_act.x2015	0.3047359

3.0.1.2 Creamos el dataset de train y test

#Creamos el dataset de train y test 

#fijamos una semilla
set.seed(583)
n <- nrow(accesin_final)
train_idx <- sample(1:n, n*0.7, replace = FALSE) # 70% para entrenamiento
train <- accesin_final[train_idx, ]
test <- accesin_final[-train_idx, ]

n_train = nrow(train)

#visualizamos la distribución
train %>% 
  group_by(installs) %>% 
  summarise(Prop = round(n()/n_train,3)) %>% 
  gt() %>%
  tab_options(page.width = "100") %>%
  tab_header(title = "Proporción de Instalaciones")

installs	Prop
Proporción de Instalaciones
0.0	0.002
1.0	0.007
5.0	0.009
10.0	0.037
50.0	0.020
100.0	0.067
500.0	0.032
1000.0	0.088
5000.0	0.045
10000.0	0.101
50000.0	0.046
100000.0	0.108
396371.7	0.050
396371.7	0.388

3.0.1.3 Modelo 1

#creamos el modelo
model <- rpart(installs ~., data = train, method = 'class')

#Graficamos
rpart.plot(model, main = "Árbol de clasificación", extra = 101, under = TRUE, branch.lty = 1, shadow.col = "gray")

#resumen del modelo creado
summary(model)

## Call:
## rpart(formula = installs ~ ., data = train, method = "class")
##   n= 7249 
## 
##           CP nsplit rel error    xerror        xstd
## 1 0.13868434      0 1.0000000 1.0000000 0.010368652
## 2 0.10702013      1 0.8613157 0.8613157 0.010444013
## 3 0.09008346      2 0.7542955 0.7557683 0.010330297
## 4 0.06504664      3 0.6642121 0.6710849 0.010129035
## 5 0.01251841      4 0.5991654 0.6072656 0.009908923
## 6 0.01202749      5 0.5866470 0.6033382 0.009893363
## 7 0.01000000      6 0.5746195 0.5915562 0.009845239
## 
## Variable importance
##          reviews     size_num_imp    ano_act.x2018   category.xGAME 
##               68               10                6                5 
## grupo_edades.x4.       rating_imp         type_bin 
##                5                4                1 
## 
## Node number 1: 7249 observations,    complexity param=0.1386843
##   predicted class=396371.74  expected loss=0.5620086  P(node) =1
##     class counts:    12    54    65   265   145   489   230   637   323   735   333   786  3175
##    probabilities: 0.002 0.007 0.009 0.037 0.020 0.067 0.032 0.088 0.045 0.101 0.046 0.108 0.438 
##   left son=2 (4013 obs) right son=3 (3236 obs)
##   Primary splits:
##       reviews       < 3430.5 to the left,  improve=1594.34500, (0 missing)
##       ano_act.x2018 < 0.5    to the left,  improve= 153.10500, (0 missing)
##       size_num_imp  < 33500  to the left,  improve= 117.21300, (0 missing)
##       type_bin      < 0.5    to the right, improve=  99.12031, (0 missing)
##       rating_imp    < 4.75   to the right, improve=  89.13282, (0 missing)
##   Surrogate splits:
##       size_num_imp     < 33500  to the left,  agree=0.636, adj=0.184, (0 split)
##       ano_act.x2018    < 0.5    to the left,  agree=0.605, adj=0.115, (0 split)
##       category.xGAME   < 0.5    to the left,  agree=0.603, adj=0.110, (0 split)
##       grupo_edades.x4. < 0.5    to the right, agree=0.598, adj=0.099, (0 split)
##       rating_imp       < 4.15   to the left,  agree=0.577, adj=0.053, (0 split)
## 
## Node number 2: 4013 observations,    complexity param=0.1070201
##   predicted class=10000      expected loss=0.817842  P(node) =0.5535936
##     class counts:    12    54    65   265   145   489   230   637   323   731   320   576   166
##    probabilities: 0.003 0.013 0.016 0.066 0.036 0.122 0.057 0.159 0.080 0.182 0.080 0.144 0.041 
##   left son=4 (2096 obs) right son=5 (1917 obs)
##   Primary splits:
##       reviews            < 57.5   to the left,  improve=331.531700, (0 missing)
##       rating_imp         < 4.95   to the right, improve= 35.459040, (0 missing)
##       type_bin           < 0.5    to the right, improve= 14.158570, (0 missing)
##       category.xBUSINESS < 0.5    to the right, improve=  7.719463, (0 missing)
##       ano_act.x2018      < 0.5    to the left,  improve=  6.210602, (0 missing)
##   Surrogate splits:
##       rating_imp       < 4.55   to the right, agree=0.555, adj=0.069, (0 split)
##       size_num_imp     < 34500  to the left,  agree=0.551, adj=0.061, (0 split)
##       android_ver_imp  < 2.65   to the right, agree=0.534, adj=0.024, (0 split)
##       category.xGAME   < 0.5    to the left,  agree=0.534, adj=0.023, (0 split)
##       grupo_edades.x4. < 0.5    to the right, agree=0.532, adj=0.020, (0 split)
## 
## Node number 3: 3236 observations
##   predicted class=396371.74  expected loss=0.07014833  P(node) =0.4464064
##     class counts:     0     0     0     0     0     0     0     0     0     4    13   210  3009
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.065 0.930 
## 
## Node number 4: 2096 observations,    complexity param=0.06504664
##   predicted class=1000       expected loss=0.740458  P(node) =0.2891433
##     class counts:    12    54    65   265   145   489   223   544   187   108     3     1     0
##    probabilities: 0.006 0.026 0.031 0.126 0.069 0.233 0.106 0.260 0.089 0.052 0.001 0.000 0.000 
##   left son=8 (987 obs) right son=9 (1109 obs)
##   Primary splits:
##       reviews          < 4.5    to the left,  improve=145.843000, (0 missing)
##       rating_imp       < 4.95   to the right, improve= 12.720960, (0 missing)
##       type_bin         < 0.5    to the right, improve=  5.845681, (0 missing)
##       category.xFAMILY < 0.5    to the left,  improve=  5.206641, (0 missing)
##       ano_act.x2018    < 0.5    to the right, improve=  4.586008, (0 missing)
##   Surrogate splits:
##       category.xBUSINESS < 0.5    to the right, agree=0.556, adj=0.057, (0 split)
##       rating_imp         < 4.95   to the right, agree=0.552, adj=0.048, (0 split)
##       ano_act.x2018      < 0.5    to the right, agree=0.549, adj=0.043, (0 split)
##       category.xMEDICAL  < 0.5    to the right, agree=0.542, adj=0.027, (0 split)
##       size_num_imp       < 7450   to the right, agree=0.539, adj=0.021, (0 split)
## 
## Node number 5: 1917 observations,    complexity param=0.09008346
##   predicted class=10000      expected loss=0.675013  P(node) =0.2644503
##     class counts:     0     0     0     0     0     0     7    93   136   623   317   575   166
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.049 0.071 0.325 0.165 0.300 0.087 
##   left son=10 (919 obs) right son=11 (998 obs)
##   Primary splits:
##       reviews           < 417.5  to the left,  improve=183.621600, (0 missing)
##       type_bin          < 0.5    to the right, improve= 32.657830, (0 missing)
##       rating_imp        < 4.45   to the right, improve= 10.123790, (0 missing)
##       category.xFINANCE < 0.5    to the right, improve=  6.843752, (0 missing)
##       size_num_imp      < 2150   to the left,  improve=  4.607771, (0 missing)
##   Surrogate splits:
##       size_num_imp  < 4350   to the left,  agree=0.560, adj=0.083, (0 split)
##       rating_imp    < 3.25   to the left,  agree=0.543, adj=0.047, (0 split)
##       ano_act.x2017 < 0.5    to the right, agree=0.543, adj=0.046, (0 split)
##       ano_act.x2018 < 0.5    to the left,  agree=0.541, adj=0.044, (0 split)
##       ano_act.x2016 < 0.5    to the right, agree=0.533, adj=0.025, (0 split)
## 
## Node number 8: 987 observations,    complexity param=0.01251841
##   predicted class=100        expected loss=0.6646403  P(node) =0.1361567
##     class counts:    12    54    63   249   118   331    87    66     3     1     2     1     0
##    probabilities: 0.012 0.055 0.064 0.252 0.120 0.335 0.088 0.067 0.003 0.001 0.002 0.001 0.000 
##   left son=16 (631 obs) right son=17 (356 obs)
##   Primary splits:
##       reviews                       < 1.5    to the left,  improve=32.162300, (0 missing)
##       type_bin                      < 0.5    to the right, improve= 7.373249, (0 missing)
##       android_ver_imp               < 2.05   to the left,  improve= 3.508581, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5    to the right, improve= 3.208907, (0 missing)
##       ano_act.x2018                 < 0.5    to the right, improve= 2.428568, (0 missing)
##   Surrogate splits:
##       rating_imp              < 4.95   to the left,  agree=0.668, adj=0.079, (0 split)
##       ano_act.x2016           < 0.5    to the left,  agree=0.644, adj=0.014, (0 split)
##       size_num_imp            < 113    to the right, agree=0.642, adj=0.008, (0 split)
##       category.xVIDEO_PLAYERS < 0.5    to the left,  agree=0.642, adj=0.008, (0 split)
## 
## Node number 9: 1109 observations
##   predicted class=1000       expected loss=0.5689811  P(node) =0.1529866
##     class counts:     0     0     2    16    27   158   136   478   184   107     1     0     0
##    probabilities: 0.000 0.000 0.002 0.014 0.024 0.142 0.123 0.431 0.166 0.096 0.001 0.000 0.000 
## 
## Node number 10: 919 observations
##   predicted class=10000      expected loss=0.4798694  P(node) =0.1267761
##     class counts:     0     0     0     0     0     0     7    93   121   478   148    63     9
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.101 0.132 0.520 0.161 0.069 0.010 
## 
## Node number 11: 998 observations,    complexity param=0.01202749
##   predicted class=100000     expected loss=0.4869739  P(node) =0.1376742
##     class counts:     0     0     0     0     0     0     0     0    15   145   169   512   157
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.015 0.145 0.169 0.513 0.157 
##   left son=22 (88 obs) right son=23 (910 obs)
##   Primary splits:
##       type_bin          < 0.5    to the right, improve=44.460350, (0 missing)
##       reviews           < 1548   to the left,  improve=25.545110, (0 missing)
##       rating_imp        < 4.55   to the right, improve=11.518250, (0 missing)
##       category.xMEDICAL < 0.5    to the right, improve= 2.541844, (0 missing)
##       size_num_imp      < 217.5  to the right, improve= 2.325753, (0 missing)
## 
## Node number 16: 631 observations
##   predicted class=10         expected loss=0.6656101  P(node) =0.08704649
##     class counts:    12    53    56   211    86   160    33    15     1     1     2     1     0
##    probabilities: 0.019 0.084 0.089 0.334 0.136 0.254 0.052 0.024 0.002 0.002 0.003 0.002 0.000 
## 
## Node number 17: 356 observations
##   predicted class=100        expected loss=0.5196629  P(node) =0.04911022
##     class counts:     0     1     7    38    32   171    54    51     2     0     0     0     0
##    probabilities: 0.000 0.003 0.020 0.107 0.090 0.480 0.152 0.143 0.006 0.000 0.000 0.000 0.000 
## 
## Node number 22: 88 observations
##   predicted class=10000      expected loss=0.375  P(node) =0.01213961
##     class counts:     0     0     0     0     0     0     0     0     8    55    19     6     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.091 0.625 0.216 0.068 0.000 
## 
## Node number 23: 910 observations
##   predicted class=100000     expected loss=0.443956  P(node) =0.1255346
##     class counts:     0     0     0     0     0     0     0     0     7    90   150   506   157
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.099 0.165 0.556 0.173

El resultado del primer modelo muestra que las variables con mayor importancia son (en el siguiente orden): reviews, size_num_imp, ano_act.x2018, category.xGAME, grupo_edades.x4., rating_imp, type

# Aplicamos el modelo a los datos de prueba
predict_test <- predict(model, test, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test$installs, predict_test)
table_mat

##            predict_test
##                0    1    5   10   50  100  500 1000 5000 10000 50000 100000
##   0            0    0    0    2    0    0    0    0    0     0     0      0
##   1            0    0    0    9    0    4    0    0    0     0     0      0
##   5            0    0    0   14    0    3    0    0    0     0     0      0
##   10           0    0    0   93    0   19    0    8    0     0     0      0
##   50           0    0    0   33    0   16    0   10    0     0     0      0
##   100          0    0    0   63    0   68    0   90    0     0     0      0
##   500          0    0    0    9    0   28    0   55    0     6     0      0
##   1000         0    0    0    4    0   23    0  184    0    41     0      1
##   5000         0    0    0    1    0    2    0   83    0    59     0      1
##   10000        0    0    0    2    0    0    0   50    0   212     0     29
##   50000        0    0    0    1    0    1    0    0    0    61     0     66
##   100000       0    0    0    1    0    0    0    1    0    39     0    206
##   396371.74    0    0    0    1    0    0    0    0    0     4     0     61
##            predict_test
##             396371.74
##   0                 0
##   1                 0
##   5                 0
##   10                0
##   50                0
##   100               0
##   500               0
##   1000              0
##   5000              0
##   10000             5
##   50000            12
##   100000           96
##   396371.74      1330

# Calculamos la precisión del modelo
accuracy_train <- function(fit) {
    predict_unseen_train <- predict(fit, train, type = 'class')
    table_mat <- table(train$installs, predict_unseen_train)
    accuracy_train <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_train
}


accuracy_test <- function(fit) {
    predict_unseen <- predict(fit, test, type = 'class')
    table_mat <- table(test$installs, predict_unseen)
    accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_Test
}


print(paste('Accuracy para train', accuracy_train(model)))

## [1] "Accuracy para train 0.677058904676507"

print(paste('Accuracy para test', accuracy_test(model)))

## [1] "Accuracy para test 0.673640167364017"

El valor de 0.67 para la exactitud (accuracy) del modelo puede considerarse relativamente bueno.

# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model, newdata = test, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test$installs))

## Confusion Matrix and Statistics
## 
##            
## pred_test      0    1    5   10   50  100  500 1000 5000 10000 50000 100000
##   0            0    0    0    0    0    0    0    0    0     0     0      0
##   1            0    0    0    0    0    0    0    0    0     0     0      0
##   5            0    0    0    0    0    0    0    0    0     0     0      0
##   10           2    9   14   93   33   63    9    4    1     2     1      1
##   50           0    0    0    0    0    0    0    0    0     0     0      0
##   100          0    4    3   19   16   68   28   23    2     0     1      0
##   500          0    0    0    0    0    0    0    0    0     0     0      0
##   1000         0    0    0    8   10   90   55  184   83    50     0      1
##   5000         0    0    0    0    0    0    0    0    0     0     0      0
##   10000        0    0    0    0    0    0    6   41   59   212    61     39
##   50000        0    0    0    0    0    0    0    0    0     0     0      0
##   100000       0    0    0    0    0    0    0    1    1    29    66    206
##   396371.74    0    0    0    0    0    0    0    0    0     5    12     96
##            
## pred_test   396371.74
##   0                 0
##   1                 0
##   5                 0
##   10                1
##   50                0
##   100               0
##   500               0
##   1000              0
##   5000              0
##   10000             4
##   50000             0
##   100000           61
##   396371.74      1330
## 
## Overall Statistics
##                                                
##                Accuracy : 0.6736               
##                  95% CI : (0.6568, 0.6901)     
##     No Information Rate : 0.4493               
##     P-Value [Acc > NIR] : < 0.00000000000000022
##                                                
##                   Kappa : 0.5626               
##                                                
##  Mcnemar's Test P-Value : NA                   
## 
## Statistics by Class:
## 
##                       Class: 0 Class: 1 Class: 5 Class: 10 Class: 50 Class: 100
## Sensitivity          0.0000000 0.000000 0.000000   0.77500   0.00000    0.30769
## Specificity          1.0000000 1.000000 1.000000   0.95313   1.00000    0.96674
## Pos Pred Value             NaN      NaN      NaN   0.39914       NaN    0.41463
## Neg Pred Value       0.9993563 0.995816 0.994528   0.99061   0.98101    0.94801
## Prevalence           0.0006437 0.004184 0.005472   0.03862   0.01899    0.07113
## Detection Rate       0.0000000 0.000000 0.000000   0.02993   0.00000    0.02189
## Detection Prevalence 0.0000000 0.000000 0.000000   0.07499   0.00000    0.05278
## Balanced Accuracy    0.5000000 0.500000 0.500000   0.86407   0.50000    0.63721
##                      Class: 500 Class: 1000 Class: 5000 Class: 10000
## Sensitivity             0.00000     0.72727     0.00000      0.71141
## Specificity             1.00000     0.89594     1.00000      0.92524
## Pos Pred Value              NaN     0.38254         NaN      0.50237
## Neg Pred Value          0.96846     0.97372     0.95301      0.96797
## Prevalence              0.03154     0.08143     0.04699      0.09591
## Detection Rate          0.00000     0.05922     0.00000      0.06823
## Detection Prevalence    0.00000     0.15481     0.00000      0.13582
## Balanced Accuracy       0.50000     0.81160     0.50000      0.81832
##                      Class: 50000 Class: 100000 Class: 396371.74
## Sensitivity               0.00000        0.6006           0.9527
## Specificity               1.00000        0.9428           0.9340
## Pos Pred Value                NaN        0.5659           0.9217
## Neg Pred Value            0.95462        0.9501           0.9603
## Prevalence                0.04538        0.1104           0.4493
## Detection Rate            0.00000        0.0663           0.4281
## Detection Prevalence      0.00000        0.1172           0.4644
## Balanced Accuracy         0.50000        0.7717           0.9433

# Tabla de contingencia
table_test <- table(test$installs, pred_test)

# Precisión por instalaciones
precision <- diag(table_test) / colSums(table_test)

# Recall por instalaciones
recall <- diag(table_test) / rowSums(table_test)

# Graficar precision y recall en un gráfico de barras
barplot(precision, ylim = c(0, 1), main = "Precisión por instalaciones", xlab = "cantidad", ylab = "Precisión")

barplot(recall, ylim = c(0, 1), main = "Recall por instalaciones", xlab = "cantidad", ylab = "Recall")

El modelo clasifica correctamente el 67,36% de las muestras. En cuanto a la matriz de confusión, muestra que el modelo tiene dificultades para clasificar correctamente las clases de muestra más bajas (0, 1 y 5) y las clases de muestra más altas (5000, 50000 y 100000).

3.0.1.4 Modelo 2

Vamos a ajustar este modelo en base a tune que prueba diferentes valores de hiperparámetros y devuelve el conjunto de valores que produce el mejor modelo. En este caso se utilizará cp para controlar la complejidad del modelo:

# Define the range of values for the cp parameter
cp_values <- seq(0.001, 0.1, by = 0.001)

# Create the tuning grid
tune_grid <- data.frame(cp = cp_values)

# Fit the model with cross-validation and the tuning grid
fit <- train(
  installs ~ .,
  data = train,
  method = "rpart",
  tuneGrid = tune_grid,
  trControl = trainControl(method = "cv", number = 10, verboseIter = TRUE)
)

## + Fold01: cp=0.001 
## - Fold01: cp=0.001 
## + Fold02: cp=0.001 
## - Fold02: cp=0.001 
## + Fold03: cp=0.001 
## - Fold03: cp=0.001 
## + Fold04: cp=0.001 
## - Fold04: cp=0.001 
## + Fold05: cp=0.001 
## - Fold05: cp=0.001 
## + Fold06: cp=0.001 
## - Fold06: cp=0.001 
## + Fold07: cp=0.001 
## - Fold07: cp=0.001 
## + Fold08: cp=0.001 
## - Fold08: cp=0.001 
## + Fold09: cp=0.001 
## - Fold09: cp=0.001 
## + Fold10: cp=0.001 
## - Fold10: cp=0.001 
## Aggregating results
## Selecting tuning parameters
## Fitting cp = 0.001 on full training set

model_2 <- rpart(installs ~ ., data = train, method = "class", control = rpart.control(cp = fit$bestTune$cp))

# Plot the decision tree
rpart.plot(model_2, extra = 1,main = "Arbol" )

summary(model_2)

## Call:
## rpart(formula = installs ~ ., data = train, method = "class", 
##     control = rpart.control(cp = fit$bestTune$cp))
##   n= 7249 
## 
##             CP nsplit rel error    xerror        xstd
## 1  0.138684340      0 1.0000000 1.0000000 0.010368652
## 2  0.107020128      1 0.8613157 0.8807069 0.010448790
## 3  0.090083456      2 0.7542955 0.7447226 0.010309711
## 4  0.065046637      3 0.6642121 0.6747668 0.010139897
## 5  0.012518409      4 0.5991654 0.6107020 0.009922342
## 6  0.012027491      5 0.5866470 0.6104566 0.009921390
## 7  0.007363770      6 0.5746195 0.5886107 0.009832867
## 8  0.002209131      7 0.5672558 0.5787923 0.009790630
## 9  0.002127311     12 0.5562101 0.5792833 0.009792779
## 10 0.001840943     15 0.5498282 0.5787923 0.009790630
## 11 0.001718213     18 0.5441826 0.5780560 0.009787401
## 12 0.001636393     20 0.5407462 0.5770741 0.009783081
## 13 0.001472754     24 0.5341188 0.5760923 0.009778745
## 14 0.001227295     27 0.5297005 0.5714286 0.009757939
## 15 0.001145475     31 0.5247914 0.5770741 0.009783081
## 16 0.001104566     34 0.5213549 0.5785469 0.009789555
## 17 0.001022746     39 0.5149730 0.5748650 0.009773304
## 18 0.001000000     45 0.5088365 0.5748650 0.009773304
## 
## Variable importance
##          reviews     size_num_imp    ano_act.x2018       rating_imp 
##               65                9                5                5 
##   category.xGAME grupo_edades.x4.         type_bin 
##                5                4                4 
## 
## Node number 1: 7249 observations,    complexity param=0.1386843
##   predicted class=396371.74  expected loss=0.5620086  P(node) =1
##     class counts:    12    54    65   265   145   489   230   637   323   735   333   786  3175
##    probabilities: 0.002 0.007 0.009 0.037 0.020 0.067 0.032 0.088 0.045 0.101 0.046 0.108 0.438 
##   left son=2 (4013 obs) right son=3 (3236 obs)
##   Primary splits:
##       reviews       < 3430.5   to the left,  improve=1594.34500, (0 missing)
##       ano_act.x2018 < 0.5      to the left,  improve= 153.10500, (0 missing)
##       size_num_imp  < 33500    to the left,  improve= 117.21300, (0 missing)
##       type_bin      < 0.5      to the right, improve=  99.12031, (0 missing)
##       rating_imp    < 4.75     to the right, improve=  89.13282, (0 missing)
##   Surrogate splits:
##       size_num_imp     < 33500    to the left,  agree=0.636, adj=0.184, (0 split)
##       ano_act.x2018    < 0.5      to the left,  agree=0.605, adj=0.115, (0 split)
##       category.xGAME   < 0.5      to the left,  agree=0.603, adj=0.110, (0 split)
##       grupo_edades.x4. < 0.5      to the right, agree=0.598, adj=0.099, (0 split)
##       rating_imp       < 4.15     to the left,  agree=0.577, adj=0.053, (0 split)
## 
## Node number 2: 4013 observations,    complexity param=0.1070201
##   predicted class=10000      expected loss=0.817842  P(node) =0.5535936
##     class counts:    12    54    65   265   145   489   230   637   323   731   320   576   166
##    probabilities: 0.003 0.013 0.016 0.066 0.036 0.122 0.057 0.159 0.080 0.182 0.080 0.144 0.041 
##   left son=4 (2096 obs) right son=5 (1917 obs)
##   Primary splits:
##       reviews            < 57.5     to the left,  improve=331.531700, (0 missing)
##       rating_imp         < 4.95     to the right, improve= 35.459040, (0 missing)
##       type_bin           < 0.5      to the right, improve= 14.158570, (0 missing)
##       category.xBUSINESS < 0.5      to the right, improve=  7.719463, (0 missing)
##       ano_act.x2018      < 0.5      to the left,  improve=  6.210602, (0 missing)
##   Surrogate splits:
##       rating_imp       < 4.55     to the right, agree=0.555, adj=0.069, (0 split)
##       size_num_imp     < 34500    to the left,  agree=0.551, adj=0.061, (0 split)
##       android_ver_imp  < 2.65     to the right, agree=0.534, adj=0.024, (0 split)
##       category.xGAME   < 0.5      to the left,  agree=0.534, adj=0.023, (0 split)
##       grupo_edades.x4. < 0.5      to the right, agree=0.532, adj=0.020, (0 split)
## 
## Node number 3: 3236 observations,    complexity param=0.002127311
##   predicted class=396371.74  expected loss=0.07014833  P(node) =0.4464064
##     class counts:     0     0     0     0     0     0     0     0     0     4    13   210  3009
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.065 0.930 
##   left son=6 (296 obs) right son=7 (2940 obs)
##   Primary splits:
##       reviews           < 6550.5   to the left,  improve=75.879300, (0 missing)
##       type_bin          < 0.5      to the right, improve=62.851410, (0 missing)
##       rating_imp        < 4.55     to the right, improve= 8.094133, (0 missing)
##       ano_act.x2018     < 0.5      to the left,  improve= 4.363969, (0 missing)
##       category.xMEDICAL < 0.5      to the right, improve= 3.610085, (0 missing)
##   Surrogate splits:
##       size_num_imp < 32       to the left,  agree=0.909, adj=0.003, (0 split)
##       rating_imp   < 2.75     to the left,  agree=0.909, adj=0.003, (0 split)
## 
## Node number 4: 2096 observations,    complexity param=0.06504664
##   predicted class=1000       expected loss=0.740458  P(node) =0.2891433
##     class counts:    12    54    65   265   145   489   223   544   187   108     3     1     0
##    probabilities: 0.006 0.026 0.031 0.126 0.069 0.233 0.106 0.260 0.089 0.052 0.001 0.000 0.000 
##   left son=8 (987 obs) right son=9 (1109 obs)
##   Primary splits:
##       reviews          < 4.5      to the left,  improve=145.843000, (0 missing)
##       rating_imp       < 4.95     to the right, improve= 12.720960, (0 missing)
##       type_bin         < 0.5      to the right, improve=  5.845681, (0 missing)
##       category.xFAMILY < 0.5      to the left,  improve=  5.206641, (0 missing)
##       ano_act.x2018    < 0.5      to the right, improve=  4.586008, (0 missing)
##   Surrogate splits:
##       category.xBUSINESS < 0.5      to the right, agree=0.556, adj=0.057, (0 split)
##       rating_imp         < 4.95     to the right, agree=0.552, adj=0.048, (0 split)
##       ano_act.x2018      < 0.5      to the right, agree=0.549, adj=0.043, (0 split)
##       category.xMEDICAL  < 0.5      to the right, agree=0.542, adj=0.027, (0 split)
##       size_num_imp       < 7450     to the right, agree=0.539, adj=0.021, (0 split)
## 
## Node number 5: 1917 observations,    complexity param=0.09008346
##   predicted class=10000      expected loss=0.675013  P(node) =0.2644503
##     class counts:     0     0     0     0     0     0     7    93   136   623   317   575   166
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.049 0.071 0.325 0.165 0.300 0.087 
##   left son=10 (919 obs) right son=11 (998 obs)
##   Primary splits:
##       reviews           < 417.5    to the left,  improve=183.621600, (0 missing)
##       type_bin          < 0.5      to the right, improve= 32.657830, (0 missing)
##       rating_imp        < 4.45     to the right, improve= 10.123790, (0 missing)
##       category.xFINANCE < 0.5      to the right, improve=  6.843752, (0 missing)
##       size_num_imp      < 2150     to the left,  improve=  4.607771, (0 missing)
##   Surrogate splits:
##       size_num_imp  < 4350     to the left,  agree=0.560, adj=0.083, (0 split)
##       rating_imp    < 3.25     to the left,  agree=0.543, adj=0.047, (0 split)
##       ano_act.x2017 < 0.5      to the right, agree=0.543, adj=0.046, (0 split)
##       ano_act.x2018 < 0.5      to the left,  agree=0.541, adj=0.044, (0 split)
##       ano_act.x2016 < 0.5      to the right, agree=0.533, adj=0.025, (0 split)
## 
## Node number 6: 296 observations,    complexity param=0.002127311
##   predicted class=396371.74  expected loss=0.4324324  P(node) =0.04083322
##     class counts:     0     0     0     0     0     0     0     0     0     4    11   113   168
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.014 0.037 0.382 0.568 
##   left son=12 (21 obs) right son=13 (275 obs)
##   Primary splits:
##       type_bin         < 0.5      to the right, improve=10.101500, (0 missing)
##       rating_imp       < 4.15     to the right, improve= 9.397326, (0 missing)
##       grupo_edades.x4. < 0.5      to the left,  improve= 3.631335, (0 missing)
##       android_ver_imp  < 2.25     to the left,  improve= 2.577301, (0 missing)
##       reviews          < 5036.5   to the left,  improve= 2.311034, (0 missing)
##   Surrogate splits:
##       android_ver_imp         < 2.15     to the left,  agree=0.936, adj=0.095, (0 split)
##       category.xENTERTAINMENT < 0.5      to the right, agree=0.936, adj=0.095, (0 split)
##       ano_act.x2014           < 0.5      to the right, agree=0.936, adj=0.095, (0 split)
##       category.xCOMMUNICATION < 0.5      to the right, agree=0.932, adj=0.048, (0 split)
## 
## Node number 7: 2940 observations,    complexity param=0.002127311
##   predicted class=396371.74  expected loss=0.03367347  P(node) =0.4055732
##     class counts:     0     0     0     0     0     0     0     0     0     0     2    97  2841
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.033 0.966 
##   left son=14 (69 obs) right son=15 (2871 obs)
##   Primary splits:
##       type_bin         < 0.5      to the right, improve=44.5395400, (0 missing)
##       rating_imp       < 4.55     to the right, improve= 5.2936860, (0 missing)
##       ano_act.x2015    < 0.5      to the right, improve= 1.0158670, (0 missing)
##       category.xFAMILY < 0.5      to the right, improve= 0.8871212, (0 missing)
##       ano_act.x2018    < 0.5      to the left,  improve= 0.6688937, (0 missing)
## 
## Node number 8: 987 observations,    complexity param=0.01251841
##   predicted class=100        expected loss=0.6646403  P(node) =0.1361567
##     class counts:    12    54    63   249   118   331    87    66     3     1     2     1     0
##    probabilities: 0.012 0.055 0.064 0.252 0.120 0.335 0.088 0.067 0.003 0.001 0.002 0.001 0.000 
##   left son=16 (631 obs) right son=17 (356 obs)
##   Primary splits:
##       reviews                       < 1.5      to the left,  improve=32.162300, (0 missing)
##       type_bin                      < 0.5      to the right, improve= 7.373249, (0 missing)
##       android_ver_imp               < 2.05     to the left,  improve= 3.508581, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, improve= 3.208907, (0 missing)
##       ano_act.x2018                 < 0.5      to the right, improve= 2.428568, (0 missing)
##   Surrogate splits:
##       rating_imp              < 4.95     to the left,  agree=0.668, adj=0.079, (0 split)
##       ano_act.x2016           < 0.5      to the left,  agree=0.644, adj=0.014, (0 split)
##       size_num_imp            < 113      to the right, agree=0.642, adj=0.008, (0 split)
##       category.xVIDEO_PLAYERS < 0.5      to the left,  agree=0.642, adj=0.008, (0 split)
## 
## Node number 9: 1109 observations,    complexity param=0.002209131
##   predicted class=1000       expected loss=0.5689811  P(node) =0.1529866
##     class counts:     0     0     2    16    27   158   136   478   184   107     1     0     0
##    probabilities: 0.000 0.000 0.002 0.014 0.024 0.142 0.123 0.431 0.166 0.096 0.001 0.000 0.000 
##   left son=18 (526 obs) right son=19 (583 obs)
##   Primary splits:
##       reviews                 < 16.5     to the left,  improve=34.778520, (0 missing)
##       rating_imp              < 4.75     to the right, improve=10.371930, (0 missing)
##       type_bin                < 0.5      to the right, improve= 9.615269, (0 missing)
##       category.xVIDEO_PLAYERS < 0.5      to the left,  improve= 3.373009, (0 missing)
##       category.xPARENTING     < 0.5      to the left,  improve= 3.149121, (0 missing)
##   Surrogate splits:
##       rating_imp                    < 4.35     to the right, agree=0.564, adj=0.080, (0 split)
##       category.xBUSINESS            < 0.5      to the right, agree=0.542, adj=0.034, (0 split)
##       category.xCOMMUNICATION       < 0.5      to the right, agree=0.537, adj=0.023, (0 split)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, agree=0.532, adj=0.013, (0 split)
##       category.xEVENTS              < 0.5      to the right, agree=0.530, adj=0.010, (0 split)
## 
## Node number 10: 919 observations,    complexity param=0.00736377
##   predicted class=10000      expected loss=0.4798694  P(node) =0.1267761
##     class counts:     0     0     0     0     0     0     7    93   121   478   148    63     9
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.101 0.132 0.520 0.161 0.069 0.010 
##   left son=20 (109 obs) right son=21 (810 obs)
##   Primary splits:
##       type_bin                    < 0.5      to the right, improve=37.068620, (0 missing)
##       reviews                     < 204.5    to the left,  improve=21.938330, (0 missing)
##       rating_imp                  < 4.75     to the right, improve=11.443230, (0 missing)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  improve= 4.832124, (0 missing)
##       category.xFINANCE           < 0.5      to the right, improve= 4.621178, (0 missing)
##   Surrogate splits:
##       size_num_imp < 37       to the left,  agree=0.882, adj=0.009, (0 split)
## 
## Node number 11: 998 observations,    complexity param=0.01202749
##   predicted class=100000     expected loss=0.4869739  P(node) =0.1376742
##     class counts:     0     0     0     0     0     0     0     0    15   145   169   512   157
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.015 0.145 0.169 0.513 0.157 
##   left son=22 (88 obs) right son=23 (910 obs)
##   Primary splits:
##       type_bin          < 0.5      to the right, improve=44.460350, (0 missing)
##       reviews           < 1548     to the left,  improve=25.545110, (0 missing)
##       rating_imp        < 4.55     to the right, improve=11.518250, (0 missing)
##       category.xMEDICAL < 0.5      to the right, improve= 2.541844, (0 missing)
##       size_num_imp      < 217.5    to the right, improve= 2.325753, (0 missing)
## 
## Node number 12: 21 observations
##   predicted class=100000     expected loss=0.3809524  P(node) =0.002896951
##     class counts:     0     0     0     0     0     0     0     0     0     2     6    13     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.095 0.286 0.619 0.000 
## 
## Node number 13: 275 observations,    complexity param=0.001104566
##   predicted class=396371.74  expected loss=0.3890909  P(node) =0.03793627
##     class counts:     0     0     0     0     0     0     0     0     0     2     5   100   168
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.018 0.364 0.611 
##   left son=26 (159 obs) right son=27 (116 obs)
##   Primary splits:
##       rating_imp        < 4.15     to the right, improve=6.909134, (0 missing)
##       grupo_edades.x4.  < 0.5      to the left,  improve=3.367080, (0 missing)
##       reviews           < 3675.5   to the right, improve=3.287658, (0 missing)
##       category.xGAME    < 0.5      to the right, improve=1.438048, (0 missing)
##       category.xMEDICAL < 0.5      to the right, improve=1.163596, (0 missing)
##   Surrogate splits:
##       android_ver_imp              < 3.15     to the right, agree=0.604, adj=0.060, (0 split)
##       category.xLIFESTYLE          < 0.5      to the left,  agree=0.593, adj=0.034, (0 split)
##       category.xTOOLS              < 0.5      to the left,  agree=0.593, adj=0.034, (0 split)
##       size_num_imp                 < 1450     to the right, agree=0.589, adj=0.026, (0 split)
##       category.xNEWS_AND_MAGAZINES < 0.5      to the left,  agree=0.589, adj=0.026, (0 split)
## 
## Node number 14: 69 observations,    complexity param=0.001472754
##   predicted class=100000     expected loss=0.4202899  P(node) =0.009518554
##     class counts:     0     0     0     0     0     0     0     0     0     0     2    40    27
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.029 0.580 0.391 
##   left son=28 (51 obs) right son=29 (18 obs)
##   Primary splits:
##       size_num_imp    < 42058.96 to the left,  improve=4.091121, (0 missing)
##       reviews         < 6673.432 to the left,  improve=3.866372, (0 missing)
##       android_ver_imp < 3.5      to the right, improve=2.254170, (0 missing)
##       rating_imp      < 4.45     to the right, improve=1.521143, (0 missing)
##       ano_act.x2016   < 0.5      to the left,  improve=1.492553, (0 missing)
## 
## Node number 15: 2871 observations
##   predicted class=396371.74  expected loss=0.01985371  P(node) =0.3960546
##     class counts:     0     0     0     0     0     0     0     0     0     0     0    57  2814
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.020 0.980 
## 
## Node number 16: 631 observations,    complexity param=0.001840943
##   predicted class=10         expected loss=0.6656101  P(node) =0.08704649
##     class counts:    12    53    56   211    86   160    33    15     1     1     2     1     0
##    probabilities: 0.019 0.084 0.089 0.334 0.136 0.254 0.052 0.024 0.002 0.002 0.003 0.002 0.000 
##   left son=32 (86 obs) right son=33 (545 obs)
##   Primary splits:
##       type_bin                      < 0.5      to the right, improve=6.551269, (0 missing)
##       reviews                       < 0.5      to the left,  improve=4.406052, (0 missing)
##       size_num_imp                  < 13500    to the left,  improve=2.459145, (0 missing)
##       android_ver_imp               < 2.05     to the left,  improve=2.426151, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, improve=2.140979, (0 missing)
##   Surrogate splits:
##       android_ver_imp < 2.05     to the left,  agree=0.873, adj=0.070, (0 split)
##       ano_act.x2014   < 0.5      to the right, agree=0.868, adj=0.035, (0 split)
## 
## Node number 17: 356 observations,    complexity param=0.001227295
##   predicted class=100        expected loss=0.5196629  P(node) =0.04911022
##     class counts:     0     1     7    38    32   171    54    51     2     0     0     0     0
##    probabilities: 0.000 0.003 0.020 0.107 0.090 0.480 0.152 0.143 0.006 0.000 0.000 0.000 0.000 
##   left son=34 (347 obs) right son=35 (9 obs)
##   Primary splits:
##       rating_imp       < 2.5      to the right, improve=3.948846, (0 missing)
##       category.xFAMILY < 0.5      to the left,  improve=2.638266, (0 missing)
##       reviews          < 2.5      to the left,  improve=2.384410, (0 missing)
##       android_ver_imp  < 2.05     to the left,  improve=2.259204, (0 missing)
##       type_bin         < 0.5      to the right, improve=2.196937, (0 missing)
## 
## Node number 18: 526 observations,    complexity param=0.002209131
##   predicted class=1000       expected loss=0.5589354  P(node) =0.07256173
##     class counts:     0     0     2    16    25   120   101   232    24     6     0     0     0
##    probabilities: 0.000 0.000 0.004 0.030 0.048 0.228 0.192 0.441 0.046 0.011 0.000 0.000 0.000 
##   left son=36 (57 obs) right son=37 (469 obs)
##   Primary splits:
##       type_bin                      < 0.5      to the right, improve=8.378135, (0 missing)
##       rating_imp                    < 4.75     to the right, improve=7.540602, (0 missing)
##       reviews                       < 10.5     to the left,  improve=6.331664, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the left,  improve=3.076515, (0 missing)
##       category.xPHOTOGRAPHY         < 0.5      to the left,  improve=2.885551, (0 missing)
##   Surrogate splits:
##       ano_act.x2014 < 0.5      to the right, agree=0.894, adj=0.018, (0 split)
## 
## Node number 19: 583 observations,    complexity param=0.002209131
##   predicted class=1000       expected loss=0.5780446  P(node) =0.08042489
##     class counts:     0     0     0     0     2    38    35   246   160   101     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.003 0.065 0.060 0.422 0.274 0.173 0.002 0.000 0.000 
##   left son=38 (68 obs) right son=39 (515 obs)
##   Primary splits:
##       type_bin                < 0.5      to the right, improve=10.077620, (0 missing)
##       reviews                 < 42.5     to the left,  improve= 7.865569, (0 missing)
##       rating_imp              < 4.55     to the right, improve= 7.076145, (0 missing)
##       category.xPARENTING     < 0.5      to the left,  improve= 2.610204, (0 missing)
##       category.xVIDEO_PLAYERS < 0.5      to the left,  improve= 2.247603, (0 missing)
##   Surrogate splits:
##       size_num_imp < 34       to the left,  agree=0.887, adj=0.029, (0 split)
## 
## Node number 20: 109 observations,    complexity param=0.001472754
##   predicted class=1000       expected loss=0.5412844  P(node) =0.01503656
##     class counts:     0     0     0     0     0     0     5    50    33    20     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.046 0.459 0.303 0.183 0.009 0.000 0.000 
##   left son=40 (55 obs) right son=41 (54 obs)
##   Primary splits:
##       reviews           < 160      to the left,  improve=5.181299, (0 missing)
##       rating_imp        < 3.65     to the right, improve=3.917017, (0 missing)
##       category.xMEDICAL < 0.5      to the left,  improve=2.706491, (0 missing)
##       android_ver_imp   < 2.05     to the right, improve=2.575239, (0 missing)
##       size_num_imp      < 344      to the right, improve=1.920693, (0 missing)
##   Surrogate splits:
##       size_num_imp            < 3650     to the left,  agree=0.578, adj=0.148, (0 split)
##       rating_imp              < 4.55     to the right, agree=0.550, adj=0.093, (0 split)
##       grupo_edades.x9.        < 0.5      to the left,  agree=0.550, adj=0.093, (0 split)
##       category.xCOMMUNICATION < 0.5      to the left,  agree=0.541, adj=0.074, (0 split)
##       category.xGAME          < 0.5      to the left,  agree=0.541, adj=0.074, (0 split)
## 
## Node number 21: 810 observations,    complexity param=0.001636393
##   predicted class=10000      expected loss=0.4345679  P(node) =0.1117396
##     class counts:     0     0     0     0     0     0     2    43    88   458   147    63     9
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.053 0.109 0.565 0.181 0.078 0.011 
##   left son=42 (523 obs) right son=43 (287 obs)
##   Primary splits:
##       reviews                     < 204.5    to the left,  improve=25.244190, (0 missing)
##       rating_imp                  < 4.75     to the right, improve= 9.250378, (0 missing)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  improve= 5.101173, (0 missing)
##       category.xFINANCE           < 0.5      to the right, improve= 4.472597, (0 missing)
##       ano_act.x2013               < 0.5      to the right, improve= 1.987642, (0 missing)
##   Surrogate splits:
##       category.xGAME      < 0.5      to the left,  agree=0.651, adj=0.014, (0 split)
##       ano_act.x2011       < 0.5      to the left,  agree=0.651, adj=0.014, (0 split)
##       android_ver_imp     < 7.05     to the left,  agree=0.649, adj=0.010, (0 split)
##       rating_imp          < 1.65     to the right, agree=0.648, adj=0.007, (0 split)
##       category.xEDUCATION < 0.5      to the left,  agree=0.648, adj=0.007, (0 split)
## 
## Node number 22: 88 observations,    complexity param=0.001227295
##   predicted class=10000      expected loss=0.375  P(node) =0.01213961
##     class counts:     0     0     0     0     0     0     0     0     8    55    19     6     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.091 0.625 0.216 0.068 0.000 
##   left son=44 (68 obs) right son=45 (20 obs)
##   Primary splits:
##       reviews                   < 1815.5   to the left,  improve=6.798128, (0 missing)
##       android_ver_imp           < 3.15     to the left,  improve=2.212196, (0 missing)
##       size_num_imp              < 4600     to the left,  improve=1.905814, (0 missing)
##       category.xTOOLS           < 0.5      to the right, improve=1.761364, (0 missing)
##       category.xPERSONALIZATION < 0.5      to the right, improve=1.266814, (0 missing)
## 
## Node number 23: 910 observations,    complexity param=0.001145475
##   predicted class=100000     expected loss=0.443956  P(node) =0.1255346
##     class counts:     0     0     0     0     0     0     0     0     7    90   150   506   157
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.099 0.165 0.556 0.173 
##   left son=46 (540 obs) right son=47 (370 obs)
##   Primary splits:
##       reviews                       < 1550.5   to the left,  improve=25.192840, (0 missing)
##       rating_imp                    < 4.55     to the right, improve= 9.129044, (0 missing)
##       category.xCOMICS              < 0.5      to the right, improve= 2.601593, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, improve= 2.319170, (0 missing)
##       category.xMEDICAL             < 0.5      to the right, improve= 2.133059, (0 missing)
##   Surrogate splits:
##       category.xSOCIAL             < 0.5      to the left,  agree=0.598, adj=0.011, (0 split)
##       category.xENTERTAINMENT      < 0.5      to the left,  agree=0.597, adj=0.008, (0 split)
##       category.xHEALTH_AND_FITNESS < 0.5      to the left,  agree=0.596, adj=0.005, (0 split)
##       category.xTRAVEL_AND_LOCAL   < 0.5      to the left,  agree=0.596, adj=0.005, (0 split)
##       category.xWEATHER            < 0.5      to the left,  agree=0.596, adj=0.005, (0 split)
## 
## Node number 26: 159 observations,    complexity param=0.001104566
##   predicted class=396371.74  expected loss=0.490566  P(node) =0.02193406
##     class counts:     0     0     0     0     0     0     0     0     0     2     4    72    81
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.013 0.025 0.453 0.509 
##   left son=52 (89 obs) right son=53 (70 obs)
##   Primary splits:
##       reviews           < 5036.5   to the left,  improve=2.541121, (0 missing)
##       rating_imp        < 4.55     to the right, improve=2.268519, (0 missing)
##       grupo_edades.x4.  < 0.5      to the left,  improve=1.890206, (0 missing)
##       android_ver_imp   < 4.05     to the left,  improve=1.504865, (0 missing)
##       category.xMEDICAL < 0.5      to the right, improve=1.295178, (0 missing)
##   Surrogate splits:
##       size_num_imp                 < 36000    to the left,  agree=0.635, adj=0.171, (0 split)
##       rating_imp                   < 4.65     to the left,  agree=0.610, adj=0.114, (0 split)
##       category.xFAMILY             < 0.5      to the left,  agree=0.610, adj=0.114, (0 split)
##       category.xFINANCE            < 0.5      to the left,  agree=0.579, adj=0.043, (0 split)
##       category.xHEALTH_AND_FITNESS < 0.5      to the left,  agree=0.579, adj=0.043, (0 split)
## 
## Node number 27: 116 observations
##   predicted class=396371.74  expected loss=0.25  P(node) =0.01600221
##     class counts:     0     0     0     0     0     0     0     0     0     0     1    28    87
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.009 0.241 0.750 
## 
## Node number 28: 51 observations
##   predicted class=100000     expected loss=0.3333333  P(node) =0.007035453
##     class counts:     0     0     0     0     0     0     0     0     0     0     2    34    15
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.039 0.667 0.294 
## 
## Node number 29: 18 observations
##   predicted class=396371.74  expected loss=0.3333333  P(node) =0.002483101
##     class counts:     0     0     0     0     0     0     0     0     0     0     0     6    12
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.333 0.667 
## 
## Node number 32: 86 observations
##   predicted class=10         expected loss=0.5581395  P(node) =0.01186371
##     class counts:     8    16     9    38     9     6     0     0     0     0     0     0     0
##    probabilities: 0.093 0.186 0.105 0.442 0.105 0.070 0.000 0.000 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 33: 545 observations,    complexity param=0.001840943
##   predicted class=10         expected loss=0.6825688  P(node) =0.07518278
##     class counts:     4    37    47   173    77   154    33    15     1     1     2     1     0
##    probabilities: 0.007 0.068 0.086 0.317 0.141 0.283 0.061 0.028 0.002 0.002 0.004 0.002 0.000 
##   left son=66 (376 obs) right son=67 (169 obs)
##   Primary splits:
##       reviews       < 0.5      to the left,  improve=3.664163, (0 missing)
##       ano_act.x2018 < 0.5      to the right, improve=2.893701, (0 missing)
##       size_num_imp  < 27500    to the left,  improve=2.672262, (0 missing)
##       ano_act.x2016 < 0.5      to the left,  improve=2.405935, (0 missing)
##       rating_imp    < 3.55     to the right, improve=2.008815, (0 missing)
##   Surrogate splits:
##       rating_imp                  < 4.95     to the left,  agree=0.734, adj=0.142, (0 split)
##       category.xSHOPPING          < 0.5      to the left,  agree=0.695, adj=0.018, (0 split)
##       ano_act.x2015               < 0.5      to the left,  agree=0.694, adj=0.012, (0 split)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  agree=0.692, adj=0.006, (0 split)
##       category.xPHOTOGRAPHY       < 0.5      to the left,  agree=0.692, adj=0.006, (0 split)
## 
## Node number 34: 347 observations
##   predicted class=100        expected loss=0.5100865  P(node) =0.04786867
##     class counts:     0     1     7    38    32   170    48    49     2     0     0     0     0
##    probabilities: 0.000 0.003 0.020 0.110 0.092 0.490 0.138 0.141 0.006 0.000 0.000 0.000 0.000 
## 
## Node number 35: 9 observations
##   predicted class=500        expected loss=0.3333333  P(node) =0.001241551
##     class counts:     0     0     0     0     0     1     6     2     0     0     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.111 0.667 0.222 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 36: 57 observations
##   predicted class=100        expected loss=0.5087719  P(node) =0.007863154
##     class counts:     0     0     0     5     4    28     8    12     0     0     0     0     0
##    probabilities: 0.000 0.000 0.000 0.088 0.070 0.491 0.140 0.211 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 37: 469 observations,    complexity param=0.001022746
##   predicted class=1000       expected loss=0.5309168  P(node) =0.06469858
##     class counts:     0     0     2    11    21    92    93   220    24     6     0     0     0
##    probabilities: 0.000 0.000 0.004 0.023 0.045 0.196 0.198 0.469 0.051 0.013 0.000 0.000 0.000 
##   left son=74 (307 obs) right son=75 (162 obs)
##   Primary splits:
##       reviews                       < 10.5     to the left,  improve=7.264448, (0 missing)
##       rating_imp                    < 4.75     to the right, improve=6.951071, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the left,  improve=3.431773, (0 missing)
##       category.xPHOTOGRAPHY         < 0.5      to the left,  improve=2.593914, (0 missing)
##       ano_act.x2018                 < 0.5      to the right, improve=2.037250, (0 missing)
##   Surrogate splits:
##       category.xPHOTOGRAPHY < 0.5      to the left,  agree=0.661, adj=0.019, (0 split)
##       size_num_imp          < 635.5    to the right, agree=0.659, adj=0.012, (0 split)
##       android_ver_imp       < 6.5      to the left,  agree=0.659, adj=0.012, (0 split)
##       ano_act.x2013         < 0.5      to the left,  agree=0.657, adj=0.006, (0 split)
## 
## Node number 38: 68 observations
##   predicted class=1000       expected loss=0.4264706  P(node) =0.009380604
##     class counts:     0     0     0     0     0    14    10    39     1     4     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.206 0.147 0.574 0.015 0.059 0.000 0.000 0.000 
## 
## Node number 39: 515 observations,    complexity param=0.002209131
##   predicted class=1000       expected loss=0.5980583  P(node) =0.07104428
##     class counts:     0     0     0     0     2    24    25   207   159    97     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.004 0.047 0.049 0.402 0.309 0.188 0.002 0.000 0.000 
##   left son=78 (133 obs) right son=79 (382 obs)
##   Primary splits:
##       rating_imp              < 4.55     to the right, improve=8.756813, (0 missing)
##       reviews                 < 44.5     to the left,  improve=8.184461, (0 missing)
##       category.xPARENTING     < 0.5      to the left,  improve=2.666829, (0 missing)
##       size_num_imp            < 2350     to the right, improve=2.080131, (0 missing)
##       category.xVIDEO_PLAYERS < 0.5      to the right, improve=1.861519, (0 missing)
##   Surrogate splits:
##       category.xEVENTS         < 0.5      to the right, agree=0.746, adj=0.015, (0 split)
##       reviews                  < 56.5     to the right, agree=0.744, adj=0.008, (0 split)
##       category.xFOOD_AND_DRINK < 0.5      to the right, agree=0.744, adj=0.008, (0 split)
## 
## Node number 40: 55 observations
##   predicted class=1000       expected loss=0.3818182  P(node) =0.007587253
##     class counts:     0     0     0     0     0     0     5    34    11     5     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.091 0.618 0.200 0.091 0.000 0.000 0.000 
## 
## Node number 41: 54 observations,    complexity param=0.001472754
##   predicted class=5000       expected loss=0.5925926  P(node) =0.007449303
##     class counts:     0     0     0     0     0     0     0    16    22    15     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.296 0.407 0.278 0.019 0.000 0.000 
##   left son=82 (35 obs) right son=83 (19 obs)
##   Primary splits:
##       rating_imp        < 4.25     to the right, improve=4.123141, (0 missing)
##       android_ver_imp   < 2.15     to the right, improve=1.466734, (0 missing)
##       size_num_imp      < 978.5    to the right, improve=1.371981, (0 missing)
##       reviews           < 251.5    to the left,  improve=1.160199, (0 missing)
##       category.xMEDICAL < 0.5      to the left,  improve=1.004728, (0 missing)
##   Surrogate splits:
##       reviews                 < 168.5    to the right, agree=0.704, adj=0.158, (0 split)
##       size_num_imp            < 344      to the right, agree=0.704, adj=0.158, (0 split)
##       category.xTOOLS         < 0.5      to the left,  agree=0.704, adj=0.158, (0 split)
##       android_ver_imp         < 4.7      to the left,  agree=0.667, adj=0.053, (0 split)
##       category.xCOMMUNICATION < 0.5      to the left,  agree=0.667, adj=0.053, (0 split)
## 
## Node number 42: 523 observations,    complexity param=0.001636393
##   predicted class=10000      expected loss=0.374761  P(node) =0.07214788
##     class counts:     0     0     0     0     0     0     2    41    85   327    48    18     2
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.078 0.163 0.625 0.092 0.034 0.004 
##   left son=84 (31 obs) right son=85 (492 obs)
##   Primary splits:
##       rating_imp                  < 4.75     to the right, improve=10.705650, (0 missing)
##       reviews                     < 85.5     to the left,  improve= 6.767054, (0 missing)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  improve= 3.237148, (0 missing)
##       category.xCOMMUNICATION     < 0.5      to the right, improve= 2.332380, (0 missing)
##       size_num_imp                < 2650     to the left,  improve= 1.724450, (0 missing)
## 
## Node number 43: 287 observations,    complexity param=0.001636393
##   predicted class=10000      expected loss=0.543554  P(node) =0.03959167
##     class counts:     0     0     0     0     0     0     0     2     3   131    99    45     7
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.010 0.456 0.345 0.157 0.024 
##   left son=86 (111 obs) right son=87 (176 obs)
##   Primary splits:
##       rating_imp        < 4.25     to the right, improve=8.547383, (0 missing)
##       category.xFINANCE < 0.5      to the right, improve=5.255432, (0 missing)
##       reviews           < 207.5    to the left,  improve=3.691115, (0 missing)
##       size_num_imp      < 7500     to the right, improve=2.970639, (0 missing)
##       category.xMEDICAL < 0.5      to the left,  improve=2.327487, (0 missing)
##   Surrogate splits:
##       reviews                       < 410.5    to the right, agree=0.627, adj=0.036, (0 split)
##       category.xLIBRARIES_AND_DEMO  < 0.5      to the right, agree=0.627, adj=0.036, (0 split)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, agree=0.624, adj=0.027, (0 split)
##       category.xNEWS_AND_MAGAZINES  < 0.5      to the right, agree=0.624, adj=0.027, (0 split)
##       category.xTRAVEL_AND_LOCAL    < 0.5      to the right, agree=0.624, adj=0.027, (0 split)
## 
## Node number 44: 68 observations
##   predicted class=10000      expected loss=0.2647059  P(node) =0.009380604
##     class counts:     0     0     0     0     0     0     0     0     8    50     9     1     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.118 0.735 0.132 0.015 0.000 
## 
## Node number 45: 20 observations
##   predicted class=50000      expected loss=0.5  P(node) =0.002759001
##     class counts:     0     0     0     0     0     0     0     0     0     5    10     5     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.250 0.500 0.250 0.000 
## 
## Node number 46: 540 observations,    complexity param=0.001145475
##   predicted class=100000     expected loss=0.45  P(node) =0.07449303
##     class counts:     0     0     0     0     0     0     0     0     6    85   119   297    33
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.011 0.157 0.220 0.550 0.061 
##   left son=92 (73 obs) right son=93 (467 obs)
##   Primary splits:
##       rating_imp                < 4.55     to the right, improve=10.760680, (0 missing)
##       reviews                   < 806.5    to the left,  improve= 9.823751, (0 missing)
##       category.xCOMICS          < 0.5      to the right, improve= 3.566737, (0 missing)
##       android_ver_imp           < 4.05     to the left,  improve= 2.356799, (0 missing)
##       category.xPERSONALIZATION < 0.5      to the right, improve= 2.134066, (0 missing)
##   Surrogate splits:
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, agree=0.87, adj=0.041, (0 split)
## 
## Node number 47: 370 observations
##   predicted class=100000     expected loss=0.4351351  P(node) =0.05104152
##     class counts:     0     0     0     0     0     0     0     0     1     5    31   209   124
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.014 0.084 0.565 0.335 
## 
## Node number 52: 89 observations,    complexity param=0.001104566
##   predicted class=100000     expected loss=0.4719101  P(node) =0.01227756
##     class counts:     0     0     0     0     0     0     0     0     0     2     2    47    38
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.022 0.022 0.528 0.427 
##   left son=104 (76 obs) right son=105 (13 obs)
##   Primary splits:
##       reviews          < 3654     to the right, improve=3.9684070, (0 missing)
##       ano_act.x2018    < 0.5      to the left,  improve=1.2613220, (0 missing)
##       size_num_imp     < 2900     to the right, improve=1.0811960, (0 missing)
##       grupo_edades.x4. < 0.5      to the left,  improve=0.8318352, (0 missing)
##       rating_imp       < 4.55     to the right, improve=0.6127940, (0 missing)
## 
## Node number 53: 70 observations
##   predicted class=396371.74  expected loss=0.3857143  P(node) =0.009656504
##     class counts:     0     0     0     0     0     0     0     0     0     0     2    25    43
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.029 0.357 0.614 
## 
## Node number 66: 376 observations,    complexity param=0.001718213
##   predicted class=10         expected loss=0.6648936  P(node) =0.05186922
##     class counts:     4    33    41   126    50    92    17     8     1     1     2     1     0
##    probabilities: 0.011 0.088 0.109 0.335 0.133 0.245 0.045 0.021 0.003 0.003 0.005 0.003 0.000 
##   left son=132 (239 obs) right son=133 (137 obs)
##   Primary splits:
##       size_num_imp               < 13500    to the left,  improve=2.365628, (0 missing)
##       ano_act.x2018              < 0.5      to the right, improve=2.185873, (0 missing)
##       rating_imp                 < 3.55     to the left,  improve=1.865445, (0 missing)
##       category.xTRAVEL_AND_LOCAL < 0.5      to the left,  improve=1.664472, (0 missing)
##       grupo_edades.x4.           < 0.5      to the left,  improve=1.631643, (0 missing)
##   Surrogate splits:
##       category.xPRODUCTIVITY     < 0.5      to the left,  agree=0.649, adj=0.036, (0 split)
##       category.xSPORTS           < 0.5      to the left,  agree=0.649, adj=0.036, (0 split)
##       category.xGAME             < 0.5      to the left,  agree=0.646, adj=0.029, (0 split)
##       category.xTRAVEL_AND_LOCAL < 0.5      to the left,  agree=0.644, adj=0.022, (0 split)
##       android_ver_imp            < 4.7      to the left,  agree=0.638, adj=0.007, (0 split)
## 
## Node number 67: 169 observations,    complexity param=0.001840943
##   predicted class=100        expected loss=0.6331361  P(node) =0.02331356
##     class counts:     0     4     6    47    27    62    16     7     0     0     0     0     0
##    probabilities: 0.000 0.024 0.036 0.278 0.160 0.367 0.095 0.041 0.000 0.000 0.000 0.000 0.000 
##   left son=134 (45 obs) right son=135 (124 obs)
##   Primary splits:
##       android_ver_imp < 4.15     to the right, improve=2.680694, (0 missing)
##       rating_imp      < 3.95     to the right, improve=2.201740, (0 missing)
##       ano_act.x2016   < 0.5      to the left,  improve=2.182554, (0 missing)
##       ano_act.x2018   < 0.5      to the right, improve=1.830705, (0 missing)
##       size_num_imp    < 42029.48 to the left,  improve=1.449943, (0 missing)
##   Surrogate splits:
##       category.xBEAUTY       < 0.5      to the right, agree=0.746, adj=0.044, (0 split)
##       size_num_imp           < 42058.96 to the right, agree=0.740, adj=0.022, (0 split)
##       category.xPRODUCTIVITY < 0.5      to the right, agree=0.740, adj=0.022, (0 split)
## 
## Node number 74: 307 observations,    complexity param=0.001022746
##   predicted class=1000       expected loss=0.6058632  P(node) =0.04235067
##     class counts:     0     0     2    10    16    70    72   121    13     3     0     0     0
##    probabilities: 0.000 0.000 0.007 0.033 0.052 0.228 0.235 0.394 0.042 0.010 0.000 0.000 0.000 
##   left son=148 (184 obs) right son=149 (123 obs)
##   Primary splits:
##       rating_imp                    < 4.15     to the right, improve=3.307040, (0 missing)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the left,  improve=2.449646, (0 missing)
##       android_ver_imp               < 4.05     to the right, improve=2.186021, (0 missing)
##       ano_act.x2018                 < 0.5      to the right, improve=2.086453, (0 missing)
##       category.xPRODUCTIVITY        < 0.5      to the right, improve=1.964938, (0 missing)
##   Surrogate splits:
##       size_num_imp                < 3050     to the right, agree=0.622, adj=0.057, (0 split)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  agree=0.612, adj=0.033, (0 split)
##       category.xTOOLS             < 0.5      to the left,  agree=0.612, adj=0.033, (0 split)
##       ano_act.x2015               < 0.5      to the left,  agree=0.612, adj=0.033, (0 split)
##       category.xPERSONALIZATION   < 0.5      to the left,  agree=0.609, adj=0.024, (0 split)
## 
## Node number 75: 162 observations,    complexity param=0.001022746
##   predicted class=1000       expected loss=0.3888889  P(node) =0.02234791
##     class counts:     0     0     0     1     5    22    21    99    11     3     0     0     0
##    probabilities: 0.000 0.000 0.000 0.006 0.031 0.136 0.130 0.611 0.068 0.019 0.000 0.000 0.000 
##   left son=150 (16 obs) right son=151 (146 obs)
##   Primary splits:
##       rating_imp      < 4.85     to the right, improve=5.840859, (0 missing)
##       size_num_imp    < 10500    to the left,  improve=2.664200, (0 missing)
##       category.xGAME  < 0.5      to the right, improve=1.284953, (0 missing)
##       android_ver_imp < 4.15     to the left,  improve=1.153390, (0 missing)
##       reviews         < 14.5     to the left,  improve=1.137499, (0 missing)
## 
## Node number 78: 133 observations
##   predicted class=1000       expected loss=0.5338346  P(node) =0.01834736
##     class counts:     0     0     0     0     2    19    16    62    22    12     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.015 0.143 0.120 0.466 0.165 0.090 0.000 0.000 0.000 
## 
## Node number 79: 382 observations,    complexity param=0.002209131
##   predicted class=1000       expected loss=0.6204188  P(node) =0.05269692
##     class counts:     0     0     0     0     0     5     9   145   137    85     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.013 0.024 0.380 0.359 0.223 0.003 0.000 0.000 
##   left son=158 (304 obs) right son=159 (78 obs)
##   Primary splits:
##       reviews                 < 44.5     to the left,  improve=10.408140, (0 missing)
##       category.xBUSINESS      < 0.5      to the left,  improve= 2.246599, (0 missing)
##       size_num_imp            < 4050     to the right, improve= 1.862363, (0 missing)
##       ano_act.x2016           < 0.5      to the right, improve= 1.643459, (0 missing)
##       category.xVIDEO_PLAYERS < 0.5      to the left,  improve= 1.529237, (0 missing)
##   Surrogate splits:
##       size_num_imp < 89.5     to the right, agree=0.798, adj=0.013, (0 split)
## 
## Node number 82: 35 observations
##   predicted class=1000       expected loss=0.5428571  P(node) =0.004828252
##     class counts:     0     0     0     0     0     0     0    16    10     9     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.457 0.286 0.257 0.000 0.000 0.000 
## 
## Node number 83: 19 observations
##   predicted class=5000       expected loss=0.3684211  P(node) =0.002621051
##     class counts:     0     0     0     0     0     0     0     0    12     6     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.632 0.316 0.053 0.000 0.000 
## 
## Node number 84: 31 observations
##   predicted class=1000       expected loss=0.5806452  P(node) =0.004276452
##     class counts:     0     0     0     0     0     0     1    13     8     6     0     3     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.032 0.419 0.258 0.194 0.000 0.097 0.000 
## 
## Node number 85: 492 observations
##   predicted class=10000      expected loss=0.347561  P(node) =0.06787143
##     class counts:     0     0     0     0     0     0     1    28    77   321    48    15     2
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.057 0.157 0.652 0.098 0.030 0.004 
## 
## Node number 86: 111 observations
##   predicted class=10000      expected loss=0.3873874  P(node) =0.01531246
##     class counts:     0     0     0     0     0     0     0     2     3    68    23    11     4
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.018 0.027 0.613 0.207 0.099 0.036 
## 
## Node number 87: 176 observations,    complexity param=0.001636393
##   predicted class=50000      expected loss=0.5681818  P(node) =0.02427921
##     class counts:     0     0     0     0     0     0     0     0     0    63    76    34     3
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.358 0.432 0.193 0.017 
##   left son=174 (107 obs) right son=175 (69 obs)
##   Primary splits:
##       reviews           < 305.5    to the left,  improve=4.926168, (0 missing)
##       category.xFINANCE < 0.5      to the right, improve=4.681243, (0 missing)
##       size_num_imp      < 7500     to the right, improve=1.830204, (0 missing)
##       android_ver_imp   < 4.15     to the right, improve=1.622348, (0 missing)
##       category.xTOOLS   < 0.5      to the left,  improve=1.167208, (0 missing)
##   Surrogate splits:
##       size_num_imp                < 2350     to the right, agree=0.631, adj=0.058, (0 split)
##       android_ver_imp             < 2.25     to the right, agree=0.619, adj=0.029, (0 split)
##       rating_imp                  < 1.8      to the right, agree=0.614, adj=0.014, (0 split)
##       category.xAUTO_AND_VEHICLES < 0.5      to the left,  agree=0.614, adj=0.014, (0 split)
##       category.xCOMMUNICATION     < 0.5      to the left,  agree=0.614, adj=0.014, (0 split)
## 
## Node number 92: 73 observations,    complexity param=0.001145475
##   predicted class=10000      expected loss=0.6438356  P(node) =0.01007035
##     class counts:     0     0     0     0     0     0     0     0     5    26    18    19     5
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.068 0.356 0.247 0.260 0.068 
##   left son=184 (32 obs) right son=185 (41 obs)
##   Primary splits:
##       reviews         < 712      to the left,  improve=3.770318, (0 missing)
##       ano_act.x2018   < 0.5      to the left,  improve=2.280535, (0 missing)
##       rating_imp      < 4.85     to the right, improve=2.175079, (0 missing)
##       ano_act.x2017   < 0.5      to the left,  improve=1.949394, (0 missing)
##       android_ver_imp < 4.7      to the right, improve=1.762142, (0 missing)
##   Surrogate splits:
##       size_num_imp              < 2050     to the left,  agree=0.644, adj=0.188, (0 split)
##       ano_act.x2018             < 0.5      to the left,  agree=0.644, adj=0.188, (0 split)
##       android_ver_imp           < 3.5      to the left,  agree=0.603, adj=0.094, (0 split)
##       category.xPERSONALIZATION < 0.5      to the right, agree=0.603, adj=0.094, (0 split)
##       ano_act.x2015             < 0.5      to the right, agree=0.603, adj=0.094, (0 split)
## 
## Node number 93: 467 observations
##   predicted class=100000     expected loss=0.4047109  P(node) =0.06442268
##     class counts:     0     0     0     0     0     0     0     0     1    59   101   278    28
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.126 0.216 0.595 0.060 
## 
## Node number 104: 76 observations
##   predicted class=100000     expected loss=0.4078947  P(node) =0.0104842
##     class counts:     0     0     0     0     0     0     0     0     0     1     2    45    28
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.013 0.026 0.592 0.368 
## 
## Node number 105: 13 observations
##   predicted class=396371.74  expected loss=0.2307692  P(node) =0.001793351
##     class counts:     0     0     0     0     0     0     0     0     0     1     0     2    10
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.077 0.000 0.154 0.769 
## 
## Node number 132: 239 observations
##   predicted class=10         expected loss=0.6192469  P(node) =0.03297006
##     class counts:     4    19    23    91    30    51    12     8     0     0     0     1     0
##    probabilities: 0.017 0.079 0.096 0.381 0.126 0.213 0.050 0.033 0.000 0.000 0.000 0.004 0.000 
## 
## Node number 133: 137 observations,    complexity param=0.001718213
##   predicted class=100        expected loss=0.7007299  P(node) =0.01889916
##     class counts:     0    14    18    35    20    41     5     0     1     1     2     0     0
##    probabilities: 0.000 0.102 0.131 0.255 0.146 0.299 0.036 0.000 0.007 0.007 0.015 0.000 0.000 
##   left son=266 (100 obs) right son=267 (37 obs)
##   Primary splits:
##       ano_act.x2018          < 0.5      to the right, improve=3.842932, (0 missing)
##       category.xSPORTS       < 0.5      to the right, improve=2.540799, (0 missing)
##       android_ver_imp        < 4.7      to the left,  improve=2.037782, (0 missing)
##       rating_imp             < 4.05     to the right, improve=1.716818, (0 missing)
##       category.xPRODUCTIVITY < 0.5      to the right, improve=1.439691, (0 missing)
##   Surrogate splits:
##       ano_act.x2017             < 0.5      to the left,  agree=0.942, adj=0.784, (0 split)
##       ano_act.x2016             < 0.5      to the left,  agree=0.774, adj=0.162, (0 split)
##       android_ver_imp           < 3.15     to the right, agree=0.759, adj=0.108, (0 split)
##       category.xFINANCE         < 0.5      to the left,  agree=0.745, adj=0.054, (0 split)
##       category.xPERSONALIZATION < 0.5      to the left,  agree=0.745, adj=0.054, (0 split)
## 
## Node number 134: 45 observations
##   predicted class=10         expected loss=0.6222222  P(node) =0.006207753
##     class counts:     0     2     1    17    10     9     3     3     0     0     0     0     0
##    probabilities: 0.000 0.044 0.022 0.378 0.222 0.200 0.067 0.067 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 135: 124 observations,    complexity param=0.001227295
##   predicted class=100        expected loss=0.5725806  P(node) =0.01710581
##     class counts:     0     2     5    30    17    53    13     4     0     0     0     0     0
##    probabilities: 0.000 0.016 0.040 0.242 0.137 0.427 0.105 0.032 0.000 0.000 0.000 0.000 0.000 
##   left son=270 (33 obs) right son=271 (91 obs)
##   Primary splits:
##       rating_imp         < 4.65     to the right, improve=2.9047190, (0 missing)
##       ano_act.x2016      < 0.5      to the left,  improve=1.3617270, (0 missing)
##       ano_act.x2018      < 0.5      to the right, improve=1.2231950, (0 missing)
##       size_num_imp       < 26500    to the left,  improve=0.9421113, (0 missing)
##       category.xBUSINESS < 0.5      to the left,  improve=0.8444905, (0 missing)
## 
## Node number 148: 184 observations,    complexity param=0.001022746
##   predicted class=1000       expected loss=0.6793478  P(node) =0.02538281
##     class counts:     0     0     2     8     9    49    45    59     9     3     0     0     0
##    probabilities: 0.000 0.000 0.011 0.043 0.049 0.266 0.245 0.321 0.049 0.016 0.000 0.000 0.000 
##   left son=296 (83 obs) right son=297 (101 obs)
##   Primary splits:
##       rating_imp         < 4.65     to the right, improve=2.381488, (0 missing)
##       reviews            < 5.5      to the left,  improve=2.056307, (0 missing)
##       size_num_imp       < 10500    to the right, improve=1.861594, (0 missing)
##       category.xBUSINESS < 0.5      to the right, improve=1.826880, (0 missing)
##       ano_act.x2018      < 0.5      to the right, improve=1.719765, (0 missing)
##   Surrogate splits:
##       category.xBUSINESS            < 0.5      to the right, agree=0.587, adj=0.084, (0 split)
##       reviews                       < 6.5      to the left,  agree=0.582, adj=0.072, (0 split)
##       category.xDATING              < 0.5      to the right, agree=0.560, adj=0.024, (0 split)
##       category.xGAME                < 0.5      to the right, agree=0.560, adj=0.024, (0 split)
##       category.xBOOKS_AND_REFERENCE < 0.5      to the right, agree=0.554, adj=0.012, (0 split)
## 
## Node number 149: 123 observations
##   predicted class=1000       expected loss=0.495935  P(node) =0.01696786
##     class counts:     0     0     0     2     7    21    27    62     4     0     0     0     0
##    probabilities: 0.000 0.000 0.000 0.016 0.057 0.171 0.220 0.504 0.033 0.000 0.000 0.000 0.000 
## 
## Node number 150: 16 observations
##   predicted class=100        expected loss=0.5  P(node) =0.002207201
##     class counts:     0     0     0     1     2     8     1     3     1     0     0     0     0
##    probabilities: 0.000 0.000 0.000 0.062 0.125 0.500 0.062 0.188 0.062 0.000 0.000 0.000 0.000 
## 
## Node number 151: 146 observations
##   predicted class=1000       expected loss=0.3424658  P(node) =0.02014071
##     class counts:     0     0     0     0     3    14    20    96    10     3     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.021 0.096 0.137 0.658 0.068 0.021 0.000 0.000 0.000 
## 
## Node number 158: 304 observations,    complexity param=0.001104566
##   predicted class=1000       expected loss=0.5559211  P(node) =0.04193682
##     class counts:     0     0     0     0     0     5     9   135    98    56     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.016 0.030 0.444 0.322 0.184 0.003 0.000 0.000 
##   left son=316 (296 obs) right son=317 (8 obs)
##   Primary splits:
##       category.xBUSINESS      < 0.5      to the left,  improve=2.836771, (0 missing)
##       reviews                 < 43.5     to the left,  improve=2.689877, (0 missing)
##       category.xVIDEO_PLAYERS < 0.5      to the left,  improve=2.498833, (0 missing)
##       category.xFAMILY        < 0.5      to the right, improve=1.767272, (0 missing)
##       size_num_imp            < 30500    to the right, improve=1.764518, (0 missing)
## 
## Node number 159: 78 observations
##   predicted class=5000       expected loss=0.5  P(node) =0.0107601
##     class counts:     0     0     0     0     0     0     0    10    39    29     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.128 0.500 0.372 0.000 0.000 0.000 
## 
## Node number 174: 107 observations
##   predicted class=10000      expected loss=0.5327103  P(node) =0.01476066
##     class counts:     0     0     0     0     0     0     0     0     0    50    43    13     1
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.467 0.402 0.121 0.009 
## 
## Node number 175: 69 observations
##   predicted class=50000      expected loss=0.5217391  P(node) =0.009518554
##     class counts:     0     0     0     0     0     0     0     0     0    13    33    21     2
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.188 0.478 0.304 0.029 
## 
## Node number 184: 32 observations
##   predicted class=10000      expected loss=0.5  P(node) =0.004414402
##     class counts:     0     0     0     0     0     0     0     0     3    16    10     2     1
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.094 0.500 0.312 0.062 0.031 
## 
## Node number 185: 41 observations
##   predicted class=100000     expected loss=0.5853659  P(node) =0.005655953
##     class counts:     0     0     0     0     0     0     0     0     2    10     8    17     4
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.049 0.244 0.195 0.415 0.098 
## 
## Node number 266: 100 observations,    complexity param=0.001227295
##   predicted class=10         expected loss=0.7  P(node) =0.01379501
##     class counts:     0    12    16    30    17    22     2     0     0     0     1     0     0
##    probabilities: 0.000 0.120 0.160 0.300 0.170 0.220 0.020 0.000 0.000 0.000 0.010 0.000 0.000 
##   left son=532 (77 obs) right son=533 (23 obs)
##   Primary splits:
##       android_ver_imp        < 4.35     to the left,  improve=2.478046, (0 missing)
##       category.xSPORTS       < 0.5      to the right, improve=1.816527, (0 missing)
##       category.xPRODUCTIVITY < 0.5      to the right, improve=1.333636, (0 missing)
##       rating_imp             < 3.75     to the right, improve=1.297381, (0 missing)
##       size_num_imp           < 21500    to the right, improve=1.295984, (0 missing)
##   Surrogate splits:
##       category.xTRAVEL_AND_LOCAL < 0.5      to the left,  agree=0.78, adj=0.043, (0 split)
## 
## Node number 267: 37 observations
##   predicted class=100        expected loss=0.4864865  P(node) =0.005104152
##     class counts:     0     2     2     5     3    19     3     0     1     1     1     0     0
##    probabilities: 0.000 0.054 0.054 0.135 0.081 0.514 0.081 0.000 0.027 0.027 0.027 0.000 0.000 
## 
## Node number 270: 33 observations
##   predicted class=10         expected loss=0.5454545  P(node) =0.004552352
##     class counts:     0     0     2    15     4    10     2     0     0     0     0     0     0
##    probabilities: 0.000 0.000 0.061 0.455 0.121 0.303 0.061 0.000 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 271: 91 observations
##   predicted class=100        expected loss=0.5274725  P(node) =0.01255346
##     class counts:     0     2     3    15    13    43    11     4     0     0     0     0     0
##    probabilities: 0.000 0.022 0.033 0.165 0.143 0.473 0.121 0.044 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 296: 83 observations,    complexity param=0.001022746
##   predicted class=1000       expected loss=0.6385542  P(node) =0.01144986
##     class counts:     0     0     2     5     6    26    12    30     2     0     0     0     0
##    probabilities: 0.000 0.000 0.024 0.060 0.072 0.313 0.145 0.361 0.024 0.000 0.000 0.000 0.000 
##   left son=592 (29 obs) right son=593 (54 obs)
##   Primary splits:
##       size_num_imp       < 11500    to the right, improve=2.498146, (0 missing)
##       category.xBUSINESS < 0.5      to the left,  improve=1.945783, (0 missing)
##       android_ver_imp    < 4.05     to the right, improve=1.930632, (0 missing)
##       rating_imp         < 4.75     to the right, improve=1.542557, (0 missing)
##       category.xFAMILY   < 0.5      to the right, improve=1.438946, (0 missing)
##   Surrogate splits:
##       android_ver_imp         < 4.15     to the right, agree=0.699, adj=0.138, (0 split)
##       category.xMEDICAL       < 0.5      to the right, agree=0.699, adj=0.138, (0 split)
##       category.xBUSINESS      < 0.5      to the right, agree=0.687, adj=0.103, (0 split)
##       category.xCOMMUNICATION < 0.5      to the right, agree=0.675, adj=0.069, (0 split)
##       category.xGAME          < 0.5      to the right, agree=0.675, adj=0.069, (0 split)
## 
## Node number 297: 101 observations,    complexity param=0.001022746
##   predicted class=500        expected loss=0.6732673  P(node) =0.01393296
##     class counts:     0     0     0     3     3    23    33    29     7     3     0     0     0
##    probabilities: 0.000 0.000 0.000 0.030 0.030 0.228 0.327 0.287 0.069 0.030 0.000 0.000 0.000 
##   left son=594 (53 obs) right son=595 (48 obs)
##   Primary splits:
##       ano_act.x2018           < 0.5      to the right, improve=2.338883, (0 missing)
##       size_num_imp            < 28500    to the left,  improve=1.620878, (0 missing)
##       category.xCOMMUNICATION < 0.5      to the left,  improve=1.553164, (0 missing)
##       reviews                 < 5.5      to the left,  improve=1.446561, (0 missing)
##       ano_act.x2016           < 0.5      to the left,  improve=1.364044, (0 missing)
##   Surrogate splits:
##       ano_act.x2017   < 0.5      to the left,  agree=0.792, adj=0.563, (0 split)
##       size_num_imp    < 6850     to the right, agree=0.683, adj=0.333, (0 split)
##       ano_act.x2016   < 0.5      to the left,  agree=0.663, adj=0.292, (0 split)
##       android_ver_imp < 4.05     to the right, agree=0.653, adj=0.271, (0 split)
##       rating_imp      < 4.45     to the right, agree=0.574, adj=0.104, (0 split)
## 
## Node number 316: 296 observations,    complexity param=0.001104566
##   predicted class=1000       expected loss=0.5506757  P(node) =0.04083322
##     class counts:     0     0     0     0     0     5     8   133    98    51     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.017 0.027 0.449 0.331 0.172 0.003 0.000 0.000 
##   left son=632 (282 obs) right son=633 (14 obs)
##   Primary splits:
##       category.xVIDEO_PLAYERS < 0.5      to the left,  improve=2.423067, (0 missing)
##       reviews                 < 43.5     to the left,  improve=2.283122, (0 missing)
##       size_num_imp            < 36500    to the right, improve=1.930457, (0 missing)
##       rating_imp              < 2.85     to the left,  improve=1.886526, (0 missing)
##       ano_act.x2018           < 0.5      to the right, improve=1.435229, (0 missing)
## 
## Node number 317: 8 observations
##   predicted class=10000      expected loss=0.375  P(node) =0.0011036
##     class counts:     0     0     0     0     0     0     1     2     0     5     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.125 0.250 0.000 0.625 0.000 0.000 0.000 
## 
## Node number 532: 77 observations
##   predicted class=10         expected loss=0.6363636  P(node) =0.01062215
##     class counts:     0    11     9    28    12    15     2     0     0     0     0     0     0
##    probabilities: 0.000 0.143 0.117 0.364 0.156 0.195 0.026 0.000 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 533: 23 observations
##   predicted class=5          expected loss=0.6956522  P(node) =0.003172851
##     class counts:     0     1     7     2     5     7     0     0     0     0     1     0     0
##    probabilities: 0.000 0.043 0.304 0.087 0.217 0.304 0.000 0.000 0.000 0.000 0.043 0.000 0.000 
## 
## Node number 592: 29 observations
##   predicted class=100        expected loss=0.5172414  P(node) =0.004000552
##     class counts:     0     0     1     2     3    14     3     6     0     0     0     0     0
##    probabilities: 0.000 0.000 0.034 0.069 0.103 0.483 0.103 0.207 0.000 0.000 0.000 0.000 0.000 
## 
## Node number 593: 54 observations
##   predicted class=1000       expected loss=0.5555556  P(node) =0.007449303
##     class counts:     0     0     1     3     3    12     9    24     2     0     0     0     0
##    probabilities: 0.000 0.000 0.019 0.056 0.056 0.222 0.167 0.444 0.037 0.000 0.000 0.000 0.000 
## 
## Node number 594: 53 observations
##   predicted class=1000       expected loss=0.6415094  P(node) =0.007311353
##     class counts:     0     0     0     3     3    12    11    19     3     2     0     0     0
##    probabilities: 0.000 0.000 0.000 0.057 0.057 0.226 0.208 0.358 0.057 0.038 0.000 0.000 0.000 
## 
## Node number 595: 48 observations
##   predicted class=500        expected loss=0.5416667  P(node) =0.006621603
##     class counts:     0     0     0     0     0    11    22    10     4     1     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.229 0.458 0.208 0.083 0.021 0.000 0.000 0.000 
## 
## Node number 632: 282 observations
##   predicted class=1000       expected loss=0.5390071  P(node) =0.03890192
##     class counts:     0     0     0     0     0     5     7   130    89    50     1     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.018 0.025 0.461 0.316 0.177 0.004 0.000 0.000 
## 
## Node number 633: 14 observations
##   predicted class=5000       expected loss=0.3571429  P(node) =0.001931301
##     class counts:     0     0     0     0     0     0     1     3     9     1     0     0     0
##    probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.071 0.214 0.643 0.071 0.000 0.000 0.000

# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_2, newdata = test, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test$installs))

## Confusion Matrix and Statistics
## 
##            
## pred_test      0    1    5   10   50  100  500 1000 5000 10000 50000 100000
##   0            0    0    0    0    0    0    0    0    0     0     0      0
##   1            0    0    0    0    0    0    0    0    0     0     0      0
##   5            0    0    1    5    0    1    0    1    0     1     0      0
##   10           2    9   11   75   25   35    5    2    1     1     1      1
##   50           0    0    0    0    0    0    0    0    0     0     0      0
##   100          0    4    4   35   31  118   36   29    3     0     1      0
##   500          0    0    1    0    1    5    6   12    1     0     0      0
##   1000         0    0    0    5    2   60   50  172   77    51     0      1
##   5000         0    0    0    0    0    0    0   15   16    13     0      0
##   10000        0    0    0    0    0    2    1   22   47   195    50     30
##   50000        0    0    0    0    0    0    0    0    0     8    14     14
##   100000       0    0    0    0    0    0    0    0    1    29    72    235
##   396371.74    0    0    0    0    0    0    0    0    0     0     3     62
##            
## pred_test   396371.74
##   0                 0
##   1                 0
##   5                 0
##   10                1
##   50                0
##   100               0
##   500               0
##   1000              0
##   5000              0
##   10000             4
##   50000             0
##   100000           87
##   396371.74      1304
## 
## Overall Statistics
##                                                
##                Accuracy : 0.6875               
##                  95% CI : (0.6708, 0.7038)     
##     No Information Rate : 0.4493               
##     P-Value [Acc > NIR] : < 0.00000000000000022
##                                                
##                   Kappa : 0.5864               
##                                                
##  Mcnemar's Test P-Value : NA                   
## 
## Statistics by Class:
## 
##                       Class: 0 Class: 1  Class: 5 Class: 10 Class: 50
## Sensitivity          0.0000000 0.000000 0.0588235   0.62500   0.00000
## Specificity          1.0000000 1.000000 0.9974110   0.96853   1.00000
## Pos Pred Value             NaN      NaN 0.1111111   0.44379       NaN
## Neg Pred Value       0.9993563 0.995816 0.9948354   0.98468   0.98101
## Prevalence           0.0006437 0.004184 0.0054715   0.03862   0.01899
## Detection Rate       0.0000000 0.000000 0.0003219   0.02414   0.00000
## Detection Prevalence 0.0000000 0.000000 0.0028967   0.05439   0.00000
## Balanced Accuracy    0.5000000 0.500000 0.5281173   0.79677   0.50000
##                      Class: 100 Class: 500 Class: 1000 Class: 5000 Class: 10000
## Sensitivity             0.53394   0.061224     0.67984     0.10959      0.65436
## Specificity             0.95045   0.993353     0.91381     0.99054      0.94446
## Pos Pred Value          0.45211   0.230769     0.41148     0.36364      0.55556
## Neg Pred Value          0.96381   0.970140     0.96988     0.95756      0.96263
## Prevalence              0.07113   0.031542     0.08143     0.04699      0.09591
## Detection Rate          0.03798   0.001931     0.05536     0.00515      0.06276
## Detection Prevalence    0.08400   0.008368     0.13453     0.01416      0.11297
## Balanced Accuracy       0.74219   0.527289     0.79682     0.55007      0.79941
##                      Class: 50000 Class: 100000 Class: 396371.74
## Sensitivity              0.099291       0.68513           0.9341
## Specificity              0.992583       0.93162           0.9620
## Pos Pred Value           0.388889       0.55425           0.9525
## Neg Pred Value           0.958645       0.95975           0.9471
## Prevalence               0.045381       0.11040           0.4493
## Detection Rate           0.004506       0.07564           0.4197
## Detection Prevalence     0.011587       0.13647           0.4406
## Balanced Accuracy        0.545937       0.80838           0.9481

predict_test <- predict(model_2, test, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test$installs, predict_test)
table_mat

##            predict_test
##                0    1    5   10   50  100  500 1000 5000 10000 50000 100000
##   0            0    0    0    2    0    0    0    0    0     0     0      0
##   1            0    0    0    9    0    4    0    0    0     0     0      0
##   5            0    0    1   11    0    4    1    0    0     0     0      0
##   10           0    0    5   75    0   35    0    5    0     0     0      0
##   50           0    0    0   25    0   31    1    2    0     0     0      0
##   100          0    0    1   35    0  118    5   60    0     2     0      0
##   500          0    0    0    5    0   36    6   50    0     1     0      0
##   1000         0    0    1    2    0   29   12  172   15    22     0      0
##   5000         0    0    0    1    0    3    1   77   16    47     0      1
##   10000        0    0    1    1    0    0    0   51   13   195     8     29
##   50000        0    0    0    1    0    1    0    0    0    50    14     72
##   100000       0    0    0    1    0    0    0    1    0    30    14    235
##   396371.74    0    0    0    1    0    0    0    0    0     4     0     87
##            predict_test
##             396371.74
##   0                 0
##   1                 0
##   5                 0
##   10                0
##   50                0
##   100               0
##   500               0
##   1000              0
##   5000              0
##   10000             0
##   50000             3
##   100000           62
##   396371.74      1304

print(paste('Accuracy para train', accuracy_train(model_2)))

## [1] "Accuracy para train 0.714029521313285"

print(paste('Accuracy para test', accuracy_test(model_2)))

## [1] "Accuracy para test 0.687479884132604"

En comparación con el modelo 2, podemos ver que el modelo 1 tiene una accuracy menor (67,36% vs 69%), un kappa menor (0,5626 vs 0.5939) y una sensibilidad mucho menor para las clases 0, 1, 5 y 50 y una sensibilidad mayor para las clases 1000, 50000 y 100000.

El accuracy tanto para train como para test son similares, lo cual es una buena señal de que no hay overfitting o sobreajuste

# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_2, newdata = test, type = "class")

# Tabla de contingencia
table_test <- table(test$installs, pred_test)

# Precisión por instalaciones
precision <- diag(table_test) / colSums(table_test)

# Recall por instalaciones
recall <- diag(table_test) / rowSums(table_test)



# Graficar precision y recall en un gráfico de barras
barplot(precision, ylim = c(0, 1), main = "Precisión por instalaciones", xlab = "cantidad", ylab = "Precisión")

barplot(recall, ylim = c(0, 1), main = "Recall por instalaciones", xlab = "cantidad", ylab = "Recall")

3.0.1.5 Arbol de decisión con la variable popular

Mas arriba se creó una variable popular (binaria) en base a installs a partir de la distribución de la cantidad de instalaciones, aquellas apps con > 100000 instalaciones se las consideró populares. Se tratará de predecir la popularidad de las apps en base a esta variable y comparar si el modelo predice mejor que con installs

#fijamos una semilla
set.seed(583)
n <- nrow(df_popular)
train_idx <- sample(1:n, n*0.7, replace = FALSE) # 70% para entrenamiento
train_pop <- df_popular[train_idx, ]
test_pop <- df_popular[-train_idx, ]

n_train = nrow(train_pop)
train_pop %>% 
  group_by(popular) %>% 
  summarise(Prop = round(n()/n_train,3)) %>% 
  gt() %>%
  tab_options(page.width = "100") %>%
  tab_header(title = "Proporción de Instalaciones")

popular	Prop
Proporción de Instalaciones
0	0.454
1	0.546

Realizamos el modelo:

#creamos el modelo
model_pop <- rpart(popular ~., data = train_pop, method = 'class')

#Graficamos el arbol
# fancyRpartPlot(model, type = 1, palettes=c("Greys", "Blues"), main = "Arbol de Clasificación - Modelo 1", caption = "Por la cantidad de instalaciones")

rpart.plot(model_pop, main = "Árbol de clasificación", extra = 101, under = TRUE, branch.lty = 1, shadow.col = "gray")

#resumen del modelo creado
summary(model_pop)

## Call:
## rpart(formula = popular ~ ., data = train_pop, method = "class")
##   n= 7249 
## 
##        CP nsplit rel error    xerror        xstd
## 1 0.88382      0   1.00000 1.0000000 0.012891322
## 2 0.01000      1   0.11618 0.1225669 0.005933352
## 
## Variable importance
##       reviews ano_act.x2018  size_num_imp    rating_imp ano_act.x2017 
##            64            10             9             7             6 
##      type_bin 
##             4 
## 
## Node number 1: 7249 observations,    complexity param=0.88382
##   predicted class=1  expected loss=0.4535798  P(node) =1
##     class counts:  3288  3961
##    probabilities: 0.454 0.546 
##   left son=2 (3160 obs) right son=3 (4089 obs)
##   Primary splits:
##       reviews       < 580.5 to the left,  improve=2871.2720, (0 missing)
##       ano_act.x2018 < 0.5   to the left,  improve= 227.5610, (0 missing)
##       size_num_imp  < 33500 to the left,  improve= 202.2597, (0 missing)
##       type_bin      < 0.5   to the right, improve= 171.8375, (0 missing)
##       rating_imp    < 4.75  to the right, improve= 162.3323, (0 missing)
##   Surrogate splits:
##       ano_act.x2018 < 0.5   to the left,  agree=0.633, adj=0.158, (0 split)
##       size_num_imp  < 5350  to the left,  agree=0.625, adj=0.140, (0 split)
##       rating_imp    < 3.75  to the left,  agree=0.612, adj=0.111, (0 split)
##       ano_act.x2017 < 0.5   to the right, agree=0.604, adj=0.092, (0 split)
##       type_bin      < 0.5   to the right, agree=0.592, adj=0.064, (0 split)
## 
## Node number 2: 3160 observations
##   predicted class=0  expected loss=0.04018987  P(node) =0.4359222
##     class counts:  3033   127
##    probabilities: 0.960 0.040 
## 
## Node number 3: 4089 observations
##   predicted class=1  expected loss=0.06236244  P(node) =0.5640778
##     class counts:   255  3834
##    probabilities: 0.062 0.938

predict_test <- predict(model_pop, test_pop, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test_pop$popular, predict_test)
table_mat

##    predict_test
##        0    1
##   0 1261  107
##   1   71 1668

accuracy_train <- function(fit) {
    predict_unseen_train <- predict(fit, train_pop, type = 'class')
    table_mat <- table(train_pop$popular, predict_unseen_train)
    accuracy_train <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_train
}


accuracy_test <- function(fit) {
    predict_unseen <- predict(fit, test_pop, type = 'class')
    table_mat <- table(test_pop$popular, predict_unseen)
    accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_Test
}

print(paste('Accuracy para train', accuracy_train(model_pop)))

## [1] "Accuracy para train 0.947303076286384"

print(paste('Accuracy para test', accuracy_test(model_pop)))

## [1] "Accuracy para test 0.942710009655616"

# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_pop, newdata = test_pop, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test_pop$popular))

## Confusion Matrix and Statistics
## 
##          
## pred_test    0    1
##         0 1261   71
##         1  107 1668
##                                                
##                Accuracy : 0.9427               
##                  95% CI : (0.934, 0.9506)      
##     No Information Rate : 0.5597               
##     P-Value [Acc > NIR] : < 0.00000000000000022
##                                                
##                   Kappa : 0.8834               
##                                                
##  Mcnemar's Test P-Value : 0.008707             
##                                                
##             Sensitivity : 0.9218               
##             Specificity : 0.9592               
##          Pos Pred Value : 0.9467               
##          Neg Pred Value : 0.9397               
##              Prevalence : 0.4403               
##          Detection Rate : 0.4059               
##    Detection Prevalence : 0.4287               
##       Balanced Accuracy : 0.9405               
##                                                
##        'Positive' Class : 0                    
##

predictions <- predict(model_pop, newdata = test, type = "prob")[, 2]


roc_curve <- roc(test_pop$popular ~ predictions)
plot(roc_curve)

auc(roc_curve)

## Area under the curve: 0.9405

Al utilizar la variable dependiente popular en lugar de installs, el modelo no toma en cuenta todas las variabilidades de installs. Sin embargo, model_pop es más preciso para la predicción de la popularidad

Respecto a la curva ROC, el AUC es de 0.9405 lo que indica que el modelo tiene una buena capacidad para clasificar

La matriz de confusión muestra que el model_pop tiene una precisión del 94.27%, con una sensibilidad del 92.18% y una especificidad del 95.92%. Además, Kappa indica una fuerte concordancia entre las predicciones del modelo y los valores reales observados.

Las posibles variables predictoras son reviews y ano_act.x2018 junto con size_num_imp, rating_imp y type_bin. La precisión del modelo es delel 94%, y la probabilidad de clasificación correcta para la 1 (popular) es de 92.18% y para 0 es de 95.92%. La gratuidad de las apps, un rating mayor y las apps con mayor tamaños son las que tienen más relación con la popularidad de las apps:

p1 <- ggplot(data = train_pop, aes(x = type_bin, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Type", y = "Popularidad") + 
  ggtitle("Popularidad x type")+
  theme_classic()  +
  theme(plot.title = element_text(size = 10))

p2 <- ggplot(data = train_pop, aes(x = rating_imp, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "rating", y = "") + 
  ggtitle("Popularidad x rating") + 
    theme_classic() + 
    theme(plot.title = element_text(size = 10))

p3 <- ggplot(data = train_pop, aes(x = size_num_imp, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "tamaño", y = "") + 
  ggtitle("Popularidad x tamaño") +
  theme_classic()  +
  theme(plot.title = element_text(size = 10))



cowplot::plot_grid(p1, p2, p3, ncol = 3, align = "h")

# Limpiamos memoria 
rm(fit, model,model_2,model_pop,p1,p2,p3, predict_test, predictions, roc1, roc2, roc_test,roc_curve, test_pop, test, train, train_pop, tune_grid, accuracy, cp_values, n, n_train, precision, pred_test, recall,table_mat, table_test, train_idx, df_analisis, accuracy_test,accuracy_Test,accuracy_train,df_final)

3.1 ¿Se puede predecir la popularidad de una APP?

3.1.1 Regresión Logística⁴

En función del objetivo del trabajo “desarrollar una app de promoción”, se buscará elaborar un modelo que permita predecir la probabilidad de que una aplicación sea popular en función de sus características, para contribuir en las decisiones sobre el desarrollo y estrategia de marketing de la App.

Vamos a utilizar df_popular

# Regresión logística
library(caTools) #muestra
library(MASS) #stepAIC

df_popular %>% 
  head(5) %>% 
  gt()

reviews	size_num_imp	rating_imp	android_ver_imp	popular	grupo_edades.x4.	ano_act.x2018
159.000	19000	4.1	4.0	0	1	1
967.000	14000	3.9	4.0	1	1	1
6673.432	8700	4.7	4.0	1	1	1
6673.432	25000	4.5	4.2	1	0	1
967.000	2800	4.3	4.4	1	1	1

#Dividimos la base en train y validation
set.seed(1120)
indices = sample.split(df_popular$popular, SplitRatio = 0.7)
train = df_popular[indices,]
validation = df_popular[!(indices),]

3.1.1.1 Modelo 1

# Primer modelo con todas las variables
model_1 = glm(popular ~ ., data = train, family = "binomial")
summary(model_1)

## 
## Call:
## glm(formula = popular ~ ., family = "binomial", data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -4.9577  -0.2944   0.0008   0.0014   3.6714  
## 
## Coefficients:
##                                    Estimate    Std. Error z value
## (Intercept)                    12.388887858 324.744348865   0.038
## reviews                         0.002559911   0.000101855  25.133
## type_bin                       -8.221826174   0.673893559 -12.200
## size_num_imp                    0.000004066   0.000004966   0.819
## rating_imp                     -0.564338309   0.086966948  -6.489
## android_ver_imp                -0.076240167   0.080436830  -0.948
## category.xAUTO_AND_VEHICLES    -0.467622446   0.566044964  -0.826
## category.xBEAUTY               -0.894271265   0.668085372  -1.339
## category.xBOOKS_AND_REFERENCE  -2.456852098   0.634579027  -3.872
## category.xBUSINESS             -2.464637006   0.517624412  -4.761
## category.xCOMICS               -2.802789589   0.929428167  -3.016
## category.xCOMMUNICATION        -1.795538738   0.537497684  -3.341
## category.xDATING               -1.923513933   0.673317979  -2.857
## category.xEDUCATION             0.155848040   0.632748728   0.246
## category.xENTERTAINMENT        -0.607821759   1.145987823  -0.530
## category.xEVENTS               -1.422233810   0.661540747  -2.150
## category.xFAMILY               -1.583373049   0.420157067  -3.769
## category.xFINANCE              -2.827766809   0.559323761  -5.056
## category.xFOOD_AND_DRINK       -0.786501355   0.568652894  -1.383
## category.xGAME                 -1.745951570   0.485280079  -3.598
## category.xHEALTH_AND_FITNESS   -1.671373480   0.533250944  -3.134
## category.xHOUSE_AND_HOME       -0.581546032   0.664851951  -0.875
## category.xLIBRARIES_AND_DEMO   -1.193724587   0.592359188  -2.015
## category.xLIFESTYLE            -1.999204222   0.493663991  -4.050
## category.xMAPS_AND_NAVIGATION  -2.099727251   0.661136272  -3.176
## category.xMEDICAL              -2.389822075   0.519288377  -4.602
## category.xNEWS_AND_MAGAZINES   -2.105287128   0.555544363  -3.790
## category.xPARENTING            -0.283102277   0.588921919  -0.481
## category.xPERSONALIZATION      -1.696018311   0.531797239  -3.189
## category.xPHOTOGRAPHY          -0.847654859   0.541144957  -1.566
## category.xPRODUCTIVITY         -1.673246295   0.515656212  -3.245
## category.xSHOPPING             -1.347994511   0.612867024  -2.199
## category.xSOCIAL               -2.959814870   0.704809941  -4.199
## category.xSPORTS               -2.379326836   0.537474975  -4.427
## category.xTOOLS                -1.412186155   0.436679753  -3.234
## category.xTRAVEL_AND_LOCAL     -1.689209355   0.557713171  -3.029
## category.xVIDEO_PLAYERS        -1.702548856   0.604605379  -2.816
## category.xWEATHER              -1.400207522   0.980858657  -1.428
## grupo_edades.x17.               0.946976626   0.509417292   1.859
## grupo_edades.x4.                0.622005764   0.265810639   2.340
## grupo_edades.x9.                0.643597338   0.486276704   1.324
## ano_act.x2011                 -10.857782891 324.745478384  -0.033
## ano_act.x2012                 -10.879129249 324.744570532  -0.034
## ano_act.x2013                 -11.941472038 324.744180856  -0.037
## ano_act.x2014                 -12.144618633 324.743963334  -0.037
## ano_act.x2015                 -11.412222280 324.743858282  -0.035
## ano_act.x2016                 -11.934297781 324.743845680  -0.037
## ano_act.x2017                 -11.959239558 324.743811356  -0.037
## ano_act.x2018                 -11.380131206 324.743811550  -0.035
##                                           Pr(>|z|)    
## (Intercept)                               0.969568    
## reviews                       < 0.0000000000000002 ***
## type_bin                      < 0.0000000000000002 ***
## size_num_imp                              0.412867    
## rating_imp                         0.0000000000863 ***
## android_ver_imp                           0.343218    
## category.xAUTO_AND_VEHICLES               0.408735    
## category.xBEAUTY                          0.180714    
## category.xBOOKS_AND_REFERENCE             0.000108 ***
## category.xBUSINESS                 0.0000019221750 ***
## category.xCOMICS                          0.002565 ** 
## category.xCOMMUNICATION                   0.000836 ***
## category.xDATING                          0.004280 ** 
## category.xEDUCATION                       0.805448    
## category.xENTERTAINMENT                   0.595841    
## category.xEVENTS                          0.031565 *  
## category.xFAMILY                          0.000164 ***
## category.xFINANCE                  0.0000004288404 ***
## category.xFOOD_AND_DRINK                  0.166636    
## category.xGAME                            0.000321 ***
## category.xHEALTH_AND_FITNESS              0.001723 ** 
## category.xHOUSE_AND_HOME                  0.381737    
## category.xLIBRARIES_AND_DEMO              0.043883 *  
## category.xLIFESTYLE                0.0000512774927 ***
## category.xMAPS_AND_NAVIGATION             0.001494 ** 
## category.xMEDICAL                  0.0000041823282 ***
## category.xNEWS_AND_MAGAZINES              0.000151 ***
## category.xPARENTING                       0.630721    
## category.xPERSONALIZATION                 0.001427 ** 
## category.xPHOTOGRAPHY                     0.117253    
## category.xPRODUCTIVITY                    0.001175 ** 
## category.xSHOPPING                        0.027843 *  
## category.xSOCIAL                   0.0000267562824 ***
## category.xSPORTS                   0.0000095614441 ***
## category.xTOOLS                           0.001221 ** 
## category.xTRAVEL_AND_LOCAL                0.002455 ** 
## category.xVIDEO_PLAYERS                   0.004863 ** 
## category.xWEATHER                         0.153426    
## grupo_edades.x17.                         0.063036 .  
## grupo_edades.x4.                          0.019282 *  
## grupo_edades.x9.                          0.185662    
## ano_act.x2011                             0.973328    
## ano_act.x2012                             0.973275    
## ano_act.x2013                             0.970667    
## ano_act.x2014                             0.970168    
## ano_act.x2015                             0.971966    
## ano_act.x2016                             0.970684    
## ano_act.x2017                             0.970623    
## ano_act.x2018                             0.972045    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9975.4  on 7248  degrees of freedom
## Residual deviance: 2011.2  on 7200  degrees of freedom
## AIC: 2109.2
## 
## Number of Fisher Scoring iterations: 11

Las variables con mayor significancia son “reviews”, “type_bin”, “rating_imp” y “category.xFINANCE”. A continuación se muestra en una tabla las variables con significancia estadística del modelo 1:

Variable	P-valor
reviews	< 0.0000000000000002
type_bin	< 0.0000000000000002
rating_imp	0.000000000256
category.xBOOKS_AND_REFERENCE	0.000120
category.xBUSINESS	0.000003146100
category.xCOMICS	0.003096
category.xCOMMUNICATION	0.001129
category.xDATING	0.006090
category.xEVENTS	0.029426
category.xFAMILY	0.000304
category.xFINANCE	0.000000543376
category.xGAME	0.000801
category.xHEALTH_AND_FITNESS	0.002626
category.xLIBRARIES_AND_DEMO	0.045199
category.xLIFESTYLE	0.000064984971
category.xMAPS_AND_NAVIGATION	0.002266
category.xMEDICAL	0.000008479370
category.xNEWS_AND_MAGAZINES	0.000208
category.xPERSONALIZATION	0.002230
category.xPRODUCTIVITY	0.001483
category.xSHOPPING	0.028897
category.xSOCIAL	0.000031306821
category.xSPORTS	0.000006654342
category.xTOOLS	0.001749
category.xTRAVEL_AND_LOCAL	0.004953
category.xVIDEO_PLAYERS	0.007778
grupo_edades.x17.	0.065640
grupo_edades.x4.	0.019739

3.1.1.2 Modelo 2

Se utilizará stepAIC para la selección de variables, se trata de un proceso iterativo que busca agregar o eliminar variables con el fin de obtener un subconjunto de variables que proporcione el modelo más óptimo. El modelo seleccionado es el que tiene el valor mínimo en el AIC

#seleccionamos el método más optimo
model_2<- stepAIC(model_1, direction = "backward", steps = 100)

## Start:  AIC=2109.23
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEDUCATION + category.xENTERTAINMENT + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xHOUSE_AND_HOME + category.xLIBRARIES_AND_DEMO + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPARENTING + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2011 + ano_act.x2012 + 
##     ano_act.x2013 + ano_act.x2014 + ano_act.x2015 + ano_act.x2016 + 
##     ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - category.xEDUCATION            1   2011.3 2107.3
## - category.xPARENTING            1   2011.5 2107.5
## - category.xENTERTAINMENT        1   2011.5 2107.5
## - ano_act.x2011                  1   2011.5 2107.5
## - ano_act.x2012                  1   2011.6 2107.6
## - ano_act.x2018                  1   2011.8 2107.8
## - ano_act.x2015                  1   2011.8 2107.8
## - size_num_imp                   1   2011.9 2107.9
## - category.xAUTO_AND_VEHICLES    1   2011.9 2107.9
## - category.xHOUSE_AND_HOME       1   2012.0 2108.0
## - ano_act.x2013                  1   2012.1 2108.1
## - ano_act.x2016                  1   2012.1 2108.1
## - ano_act.x2017                  1   2012.1 2108.1
## - android_ver_imp                1   2012.1 2108.1
## - ano_act.x2014                  1   2012.2 2108.2
## - grupo_edades.x9.               1   2012.9 2108.9
## - category.xBEAUTY               1   2013.1 2109.1
## - category.xFOOD_AND_DRINK       1   2013.2 2109.2
## <none>                               2011.2 2109.2
## - category.xWEATHER              1   2013.4 2109.4
## - category.xPHOTOGRAPHY          1   2013.7 2109.7
## - grupo_edades.x17.              1   2014.5 2110.5
## - category.xLIBRARIES_AND_DEMO   1   2015.4 2111.4
## - category.xEVENTS               1   2016.2 2112.2
## - category.xSHOPPING             1   2016.3 2112.3
## - grupo_edades.x4.               1   2017.1 2113.1
## - category.xDATING               1   2019.4 2115.4
## - category.xVIDEO_PLAYERS        1   2019.4 2115.4
## - category.xTRAVEL_AND_LOCAL     1   2020.5 2116.5
## - category.xTOOLS                1   2020.8 2116.8
## - category.xHEALTH_AND_FITNESS   1   2021.0 2117.0
## - category.xPERSONALIZATION      1   2021.3 2117.3
## - category.xPRODUCTIVITY         1   2021.5 2117.5
## - category.xCOMICS               1   2022.2 2118.2
## - category.xCOMMUNICATION        1   2022.3 2118.3
## - category.xMAPS_AND_NAVIGATION  1   2022.4 2118.4
## - category.xGAME                 1   2023.4 2119.4
## - category.xFAMILY               1   2023.8 2119.8
## - category.xNEWS_AND_MAGAZINES   1   2025.6 2121.6
## - category.xLIFESTYLE            1   2026.7 2122.7
## - category.xBOOKS_AND_REFERENCE  1   2027.2 2123.2
## - category.xSPORTS               1   2030.1 2126.1
## - category.xSOCIAL               1   2031.1 2127.1
## - category.xMEDICAL              1   2031.6 2127.6
## - category.xBUSINESS             1   2033.0 2129.0
## - category.xFINANCE              1   2036.8 2132.8
## - rating_imp                     1   2050.9 2146.9
## - type_bin                       1   2324.2 2420.2
## - reviews                        1   7989.8 8085.8
## 
## Step:  AIC=2107.29
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xENTERTAINMENT + category.xEVENTS + 
##     category.xFAMILY + category.xFINANCE + category.xFOOD_AND_DRINK + 
##     category.xGAME + category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPARENTING + 
##     category.xPERSONALIZATION + category.xPHOTOGRAPHY + category.xPRODUCTIVITY + 
##     category.xSHOPPING + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     category.xWEATHER + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2011 + ano_act.x2012 + ano_act.x2013 + 
##     ano_act.x2014 + ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + 
##     ano_act.x2018
## 
##                                 Df Deviance    AIC
## - ano_act.x2011                  1   2011.6 2105.6
## - ano_act.x2012                  1   2011.6 2105.6
## - category.xENTERTAINMENT        1   2011.6 2105.6
## - category.xPARENTING            1   2011.7 2105.7
## - ano_act.x2018                  1   2011.8 2105.8
## - ano_act.x2015                  1   2011.8 2105.8
## - size_num_imp                   1   2012.0 2106.0
## - ano_act.x2013                  1   2012.1 2106.1
## - ano_act.x2016                  1   2012.1 2106.1
## - ano_act.x2017                  1   2012.2 2106.2
## - android_ver_imp                1   2012.2 2106.2
## - ano_act.x2014                  1   2012.3 2106.3
## - category.xAUTO_AND_VEHICLES    1   2012.4 2106.4
## - category.xHOUSE_AND_HOME       1   2012.4 2106.4
## - grupo_edades.x9.               1   2013.0 2107.0
## <none>                               2011.3 2107.3
## - category.xBEAUTY               1   2013.9 2107.9
## - category.xWEATHER              1   2013.9 2107.9
## - category.xFOOD_AND_DRINK       1   2014.2 2108.2
## - grupo_edades.x17.              1   2014.7 2108.7
## - category.xPHOTOGRAPHY          1   2015.0 2109.0
## - category.xLIBRARIES_AND_DEMO   1   2017.1 2111.1
## - grupo_edades.x4.               1   2017.2 2111.2
## - category.xEVENTS               1   2018.1 2112.1
## - category.xSHOPPING             1   2018.4 2112.4
## - category.xDATING               1   2022.0 2116.0
## - category.xVIDEO_PLAYERS        1   2022.8 2116.8
## - category.xCOMICS               1   2024.5 2118.5
## - category.xTRAVEL_AND_LOCAL     1   2025.1 2119.1
## - category.xHEALTH_AND_FITNESS   1   2026.1 2120.1
## - category.xMAPS_AND_NAVIGATION  1   2026.5 2120.5
## - category.xPERSONALIZATION      1   2026.7 2120.7
## - category.xPRODUCTIVITY         1   2027.2 2121.2
## - category.xCOMMUNICATION        1   2028.1 2122.1
## - category.xTOOLS                1   2028.2 2122.2
## - category.xGAME                 1   2031.3 2125.3
## - category.xNEWS_AND_MAGAZINES   1   2032.6 2126.6
## - category.xBOOKS_AND_REFERENCE  1   2033.7 2127.7
## - category.xFAMILY               1   2034.7 2128.7
## - category.xLIFESTYLE            1   2036.1 2130.1
## - category.xSOCIAL               1   2038.0 2132.0
## - category.xSPORTS               1   2039.7 2133.7
## - category.xMEDICAL              1   2043.5 2137.5
## - category.xBUSINESS             1   2046.0 2140.0
## - category.xFINANCE              1   2050.4 2144.4
## - rating_imp                     1   2051.0 2145.0
## - type_bin                       1   2324.8 2418.8
## - reviews                        1   8013.7 8107.7
## 
## Step:  AIC=2105.6
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xENTERTAINMENT + category.xEVENTS + 
##     category.xFAMILY + category.xFINANCE + category.xFOOD_AND_DRINK + 
##     category.xGAME + category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPARENTING + 
##     category.xPERSONALIZATION + category.xPHOTOGRAPHY + category.xPRODUCTIVITY + 
##     category.xSHOPPING + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     category.xWEATHER + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2012 + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - ano_act.x2012                  1   2011.6 2103.6
## - category.xENTERTAINMENT        1   2011.9 2103.9
## - category.xPARENTING            1   2012.0 2104.0
## - ano_act.x2018                  1   2012.0 2104.0
## - ano_act.x2015                  1   2012.1 2104.1
## - size_num_imp                   1   2012.3 2104.3
## - android_ver_imp                1   2012.5 2104.5
## - category.xAUTO_AND_VEHICLES    1   2012.7 2104.7
## - category.xHOUSE_AND_HOME       1   2012.7 2104.7
## - ano_act.x2013                  1   2012.8 2104.8
## - ano_act.x2016                  1   2013.0 2105.0
## - ano_act.x2017                  1   2013.1 2105.1
## - grupo_edades.x9.               1   2013.3 2105.3
## - ano_act.x2014                  1   2013.4 2105.4
## <none>                               2011.6 2105.6
## - category.xBEAUTY               1   2014.2 2106.2
## - category.xWEATHER              1   2014.2 2106.2
## - category.xFOOD_AND_DRINK       1   2014.5 2106.5
## - grupo_edades.x17.              1   2015.0 2107.0
## - category.xPHOTOGRAPHY          1   2015.3 2107.3
## - category.xLIBRARIES_AND_DEMO   1   2017.4 2109.4
## - grupo_edades.x4.               1   2017.5 2109.5
## - category.xEVENTS               1   2018.4 2110.4
## - category.xSHOPPING             1   2018.7 2110.7
## - category.xDATING               1   2022.3 2114.3
## - category.xVIDEO_PLAYERS        1   2023.1 2115.1
## - category.xCOMICS               1   2024.8 2116.8
## - category.xTRAVEL_AND_LOCAL     1   2025.4 2117.4
## - category.xHEALTH_AND_FITNESS   1   2026.4 2118.4
## - category.xMAPS_AND_NAVIGATION  1   2026.8 2118.8
## - category.xPERSONALIZATION      1   2027.0 2119.0
## - category.xPRODUCTIVITY         1   2027.5 2119.5
## - category.xCOMMUNICATION        1   2028.4 2120.4
## - category.xTOOLS                1   2028.6 2120.6
## - category.xGAME                 1   2031.7 2123.7
## - category.xNEWS_AND_MAGAZINES   1   2032.9 2124.9
## - category.xBOOKS_AND_REFERENCE  1   2034.0 2126.0
## - category.xFAMILY               1   2034.9 2126.9
## - category.xLIFESTYLE            1   2036.4 2128.4
## - category.xSOCIAL               1   2038.3 2130.3
## - category.xSPORTS               1   2040.0 2132.0
## - category.xMEDICAL              1   2043.8 2135.8
## - category.xBUSINESS             1   2046.3 2138.3
## - category.xFINANCE              1   2050.7 2142.7
## - rating_imp                     1   2051.3 2143.3
## - type_bin                       1   2325.5 2417.5
## - reviews                        1   8014.8 8106.8
## 
## Step:  AIC=2103.62
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xENTERTAINMENT + category.xEVENTS + 
##     category.xFAMILY + category.xFINANCE + category.xFOOD_AND_DRINK + 
##     category.xGAME + category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPARENTING + 
##     category.xPERSONALIZATION + category.xPHOTOGRAPHY + category.xPRODUCTIVITY + 
##     category.xSHOPPING + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     category.xWEATHER + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + ano_act.x2015 + 
##     ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - category.xENTERTAINMENT        1   2012.0 2102.0
## - category.xPARENTING            1   2012.0 2102.0
## - size_num_imp                   1   2012.3 2102.3
## - ano_act.x2018                  1   2012.4 2102.4
## - ano_act.x2015                  1   2012.4 2102.4
## - android_ver_imp                1   2012.5 2102.5
## - category.xAUTO_AND_VEHICLES    1   2012.7 2102.7
## - category.xHOUSE_AND_HOME       1   2012.7 2102.7
## - grupo_edades.x9.               1   2013.3 2103.3
## - ano_act.x2013                  1   2013.6 2103.6
## <none>                               2011.6 2103.6
## - category.xBEAUTY               1   2014.2 2104.2
## - category.xWEATHER              1   2014.2 2104.2
## - category.xFOOD_AND_DRINK       1   2014.5 2104.5
## - ano_act.x2016                  1   2014.5 2104.5
## - ano_act.x2017                  1   2014.8 2104.8
## - grupo_edades.x17.              1   2015.0 2105.0
## - ano_act.x2014                  1   2015.1 2105.1
## - category.xPHOTOGRAPHY          1   2015.4 2105.4
## - category.xLIBRARIES_AND_DEMO   1   2017.5 2107.5
## - grupo_edades.x4.               1   2017.5 2107.5
## - category.xEVENTS               1   2018.4 2108.4
## - category.xSHOPPING             1   2018.7 2108.7
## - category.xDATING               1   2022.3 2112.3
## - category.xVIDEO_PLAYERS        1   2023.1 2113.1
## - category.xCOMICS               1   2024.8 2114.8
## - category.xTRAVEL_AND_LOCAL     1   2025.4 2115.4
## - category.xHEALTH_AND_FITNESS   1   2026.4 2116.4
## - category.xMAPS_AND_NAVIGATION  1   2026.8 2116.8
## - category.xPERSONALIZATION      1   2027.0 2117.0
## - category.xPRODUCTIVITY         1   2027.5 2117.5
## - category.xCOMMUNICATION        1   2028.5 2118.5
## - category.xTOOLS                1   2028.6 2118.6
## - category.xGAME                 1   2031.7 2121.7
## - category.xNEWS_AND_MAGAZINES   1   2032.9 2122.9
## - category.xBOOKS_AND_REFERENCE  1   2034.0 2124.0
## - category.xFAMILY               1   2035.0 2125.0
## - category.xLIFESTYLE            1   2036.4 2126.4
## - category.xSOCIAL               1   2038.3 2128.3
## - category.xSPORTS               1   2040.0 2130.0
## - category.xMEDICAL              1   2043.8 2133.8
## - category.xBUSINESS             1   2046.3 2136.3
## - category.xFINANCE              1   2050.7 2140.7
## - rating_imp                     1   2051.3 2141.3
## - type_bin                       1   2325.5 2415.5
## - reviews                        1   8014.9 8104.9
## 
## Step:  AIC=2101.96
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xFOOD_AND_DRINK + category.xGAME + 
##     category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPARENTING + 
##     category.xPERSONALIZATION + category.xPHOTOGRAPHY + category.xPRODUCTIVITY + 
##     category.xSHOPPING + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     category.xWEATHER + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + ano_act.x2015 + 
##     ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - category.xPARENTING            1   2012.3 2100.3
## - size_num_imp                   1   2012.6 2100.6
## - ano_act.x2018                  1   2012.7 2100.7
## - ano_act.x2015                  1   2012.8 2100.8
## - category.xAUTO_AND_VEHICLES    1   2012.9 2100.9
## - android_ver_imp                1   2012.9 2100.9
## - category.xHOUSE_AND_HOME       1   2012.9 2100.9
## - grupo_edades.x9.               1   2013.7 2101.7
## - ano_act.x2013                  1   2013.9 2101.9
## <none>                               2012.0 2102.0
## - category.xBEAUTY               1   2014.3 2102.3
## - category.xWEATHER              1   2014.4 2102.4
## - category.xFOOD_AND_DRINK       1   2014.6 2102.6
## - ano_act.x2016                  1   2014.8 2102.8
## - ano_act.x2017                  1   2015.2 2103.2
## - ano_act.x2014                  1   2015.4 2103.4
## - category.xPHOTOGRAPHY          1   2015.4 2103.4
## - grupo_edades.x17.              1   2015.4 2103.4
## - category.xLIBRARIES_AND_DEMO   1   2017.5 2105.5
## - grupo_edades.x4.               1   2018.2 2106.2
## - category.xEVENTS               1   2018.4 2106.4
## - category.xSHOPPING             1   2018.7 2106.7
## - category.xDATING               1   2022.3 2110.3
## - category.xVIDEO_PLAYERS        1   2023.1 2111.1
## - category.xCOMICS               1   2024.8 2112.8
## - category.xTRAVEL_AND_LOCAL     1   2025.4 2113.4
## - category.xHEALTH_AND_FITNESS   1   2026.4 2114.4
## - category.xMAPS_AND_NAVIGATION  1   2026.8 2114.8
## - category.xPERSONALIZATION      1   2027.1 2115.1
## - category.xPRODUCTIVITY         1   2027.6 2115.6
## - category.xCOMMUNICATION        1   2028.5 2116.5
## - category.xTOOLS                1   2028.8 2116.8
## - category.xGAME                 1   2032.0 2120.0
## - category.xNEWS_AND_MAGAZINES   1   2033.0 2121.0
## - category.xBOOKS_AND_REFERENCE  1   2034.1 2122.1
## - category.xFAMILY               1   2035.5 2123.5
## - category.xLIFESTYLE            1   2036.8 2124.8
## - category.xSOCIAL               1   2038.5 2126.5
## - category.xSPORTS               1   2040.3 2128.3
## - category.xMEDICAL              1   2044.4 2132.4
## - category.xBUSINESS             1   2046.9 2134.9
## - category.xFINANCE              1   2051.4 2139.4
## - rating_imp                     1   2051.4 2139.4
## - type_bin                       1   2325.6 2413.6
## - reviews                        1   8025.4 8113.4
## 
## Step:  AIC=2100.28
## popular ~ reviews + type_bin + size_num_imp + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xFOOD_AND_DRINK + category.xGAME + 
##     category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - size_num_imp                   1   2012.9 2098.9
## - category.xAUTO_AND_VEHICLES    1   2013.0 2099.0
## - category.xHOUSE_AND_HOME       1   2013.0 2099.0
## - ano_act.x2018                  1   2013.1 2099.1
## - ano_act.x2015                  1   2013.1 2099.1
## - android_ver_imp                1   2013.3 2099.3
## - grupo_edades.x9.               1   2014.0 2100.0
## - ano_act.x2013                  1   2014.2 2100.2
## <none>                               2012.3 2100.3
## - category.xBEAUTY               1   2014.3 2100.3
## - category.xWEATHER              1   2014.5 2100.5
## - category.xFOOD_AND_DRINK       1   2014.6 2100.6
## - ano_act.x2016                  1   2015.2 2101.2
## - ano_act.x2017                  1   2015.4 2101.4
## - category.xPHOTOGRAPHY          1   2015.4 2101.4
## - ano_act.x2014                  1   2015.7 2101.7
## - grupo_edades.x17.              1   2015.8 2101.8
## - category.xLIBRARIES_AND_DEMO   1   2017.6 2103.6
## - category.xEVENTS               1   2018.5 2104.5
## - grupo_edades.x4.               1   2018.5 2104.5
## - category.xSHOPPING             1   2018.9 2104.9
## - category.xDATING               1   2022.4 2108.4
## - category.xVIDEO_PLAYERS        1   2023.5 2109.5
## - category.xCOMICS               1   2024.9 2110.9
## - category.xTRAVEL_AND_LOCAL     1   2026.3 2112.3
## - category.xMAPS_AND_NAVIGATION  1   2027.4 2113.4
## - category.xHEALTH_AND_FITNESS   1   2027.5 2113.5
## - category.xPERSONALIZATION      1   2028.2 2114.2
## - category.xPRODUCTIVITY         1   2029.0 2115.0
## - category.xCOMMUNICATION        1   2029.8 2115.8
## - category.xTOOLS                1   2031.5 2117.5
## - category.xGAME                 1   2034.3 2120.3
## - category.xNEWS_AND_MAGAZINES   1   2034.8 2120.8
## - category.xBOOKS_AND_REFERENCE  1   2035.5 2121.5
## - category.xSOCIAL               1   2039.9 2125.9
## - category.xLIFESTYLE            1   2039.9 2125.9
## - category.xFAMILY               1   2040.7 2126.7
## - category.xSPORTS               1   2043.1 2129.1
## - category.xMEDICAL              1   2048.8 2134.8
## - rating_imp                     1   2051.9 2137.9
## - category.xBUSINESS             1   2051.9 2137.9
## - category.xFINANCE              1   2056.3 2142.3
## - type_bin                       1   2325.8 2411.8
## - reviews                        1   8040.5 8126.5
## 
## Step:  AIC=2098.95
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xAUTO_AND_VEHICLES + category.xBEAUTY + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xFOOD_AND_DRINK + category.xGAME + 
##     category.xHEALTH_AND_FITNESS + category.xHOUSE_AND_HOME + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - category.xAUTO_AND_VEHICLES    1   2013.6 2097.6
## - ano_act.x2018                  1   2013.6 2097.6
## - ano_act.x2015                  1   2013.7 2097.7
## - category.xHOUSE_AND_HOME       1   2013.7 2097.7
## - android_ver_imp                1   2013.8 2097.8
## - grupo_edades.x9.               1   2014.7 2098.7
## - ano_act.x2013                  1   2014.9 2098.9
## <none>                               2012.9 2098.9
## - category.xWEATHER              1   2015.1 2099.1
## - category.xBEAUTY               1   2015.1 2099.1
## - category.xFOOD_AND_DRINK       1   2015.2 2099.2
## - ano_act.x2016                  1   2015.7 2099.7
## - ano_act.x2017                  1   2015.9 2099.9
## - ano_act.x2014                  1   2016.3 2100.3
## - category.xPHOTOGRAPHY          1   2016.3 2100.3
## - grupo_edades.x17.              1   2016.4 2100.4
## - category.xLIBRARIES_AND_DEMO   1   2018.4 2102.4
## - grupo_edades.x4.               1   2018.9 2102.9
## - category.xEVENTS               1   2019.2 2103.2
## - category.xSHOPPING             1   2019.8 2103.8
## - category.xDATING               1   2023.3 2107.3
## - category.xVIDEO_PLAYERS        1   2024.3 2108.3
## - category.xCOMICS               1   2025.8 2109.8
## - category.xTRAVEL_AND_LOCAL     1   2026.7 2110.7
## - category.xMAPS_AND_NAVIGATION  1   2028.2 2112.2
## - category.xHEALTH_AND_FITNESS   1   2028.3 2112.3
## - category.xPERSONALIZATION      1   2029.3 2113.3
## - category.xPRODUCTIVITY         1   2029.9 2113.9
## - category.xCOMMUNICATION        1   2030.8 2114.8
## - category.xTOOLS                1   2032.8 2116.8
## - category.xGAME                 1   2034.3 2118.3
## - category.xNEWS_AND_MAGAZINES   1   2036.1 2120.1
## - category.xBOOKS_AND_REFERENCE  1   2036.5 2120.5
## - category.xLIFESTYLE            1   2040.9 2124.9
## - category.xFAMILY               1   2041.2 2125.2
## - category.xSOCIAL               1   2041.2 2125.2
## - category.xSPORTS               1   2043.8 2127.8
## - category.xMEDICAL              1   2049.2 2133.2
## - rating_imp                     1   2053.0 2137.0
## - category.xBUSINESS             1   2053.0 2137.0
## - category.xFINANCE              1   2057.7 2141.7
## - type_bin                       1   2325.8 2409.8
## - reviews                        1   8328.4 8412.4
## 
## Step:  AIC=2097.59
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xBEAUTY + category.xBOOKS_AND_REFERENCE + category.xBUSINESS + 
##     category.xCOMICS + category.xCOMMUNICATION + category.xDATING + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xHOUSE_AND_HOME + category.xLIBRARIES_AND_DEMO + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - category.xHOUSE_AND_HOME       1   2014.1 2096.1
## - ano_act.x2018                  1   2014.3 2096.3
## - ano_act.x2015                  1   2014.3 2096.3
## - android_ver_imp                1   2014.4 2096.4
## - grupo_edades.x9.               1   2015.3 2097.3
## - category.xBEAUTY               1   2015.3 2097.3
## - category.xFOOD_AND_DRINK       1   2015.4 2097.4
## - category.xWEATHER              1   2015.5 2097.5
## - ano_act.x2013                  1   2015.5 2097.5
## <none>                               2013.6 2097.6
## - ano_act.x2016                  1   2016.3 2098.3
## - category.xPHOTOGRAPHY          1   2016.4 2098.4
## - ano_act.x2017                  1   2016.6 2098.6
## - ano_act.x2014                  1   2016.9 2098.9
## - grupo_edades.x17.              1   2017.0 2099.0
## - category.xLIBRARIES_AND_DEMO   1   2018.4 2100.4
## - category.xEVENTS               1   2019.3 2101.3
## - grupo_edades.x4.               1   2019.5 2101.5
## - category.xSHOPPING             1   2019.8 2101.8
## - category.xDATING               1   2023.3 2105.3
## - category.xVIDEO_PLAYERS        1   2024.3 2106.3
## - category.xCOMICS               1   2025.8 2107.8
## - category.xTRAVEL_AND_LOCAL     1   2026.8 2108.8
## - category.xMAPS_AND_NAVIGATION  1   2028.3 2110.3
## - category.xHEALTH_AND_FITNESS   1   2028.6 2110.6
## - category.xPERSONALIZATION      1   2029.7 2111.7
## - category.xPRODUCTIVITY         1   2030.4 2112.4
## - category.xCOMMUNICATION        1   2031.2 2113.2
## - category.xTOOLS                1   2034.4 2116.4
## - category.xGAME                 1   2035.3 2117.3
## - category.xNEWS_AND_MAGAZINES   1   2036.8 2118.8
## - category.xBOOKS_AND_REFERENCE  1   2036.9 2118.9
## - category.xSOCIAL               1   2041.6 2123.6
## - category.xLIFESTYLE            1   2042.5 2124.5
## - category.xFAMILY               1   2044.7 2126.7
## - category.xSPORTS               1   2045.1 2127.1
## - category.xMEDICAL              1   2051.7 2133.7
## - rating_imp                     1   2053.3 2135.3
## - category.xBUSINESS             1   2056.1 2138.1
## - category.xFINANCE              1   2060.5 2142.5
## - type_bin                       1   2326.6 2408.6
## - reviews                        1   8344.1 8426.1
## 
## Step:  AIC=2096.1
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xBEAUTY + category.xBOOKS_AND_REFERENCE + category.xBUSINESS + 
##     category.xCOMICS + category.xCOMMUNICATION + category.xDATING + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017 + ano_act.x2018
## 
##                                 Df Deviance    AIC
## - ano_act.x2018                  1   2014.8 2094.8
## - ano_act.x2015                  1   2014.9 2094.9
## - android_ver_imp                1   2014.9 2094.9
## - category.xFOOD_AND_DRINK       1   2015.6 2095.6
## - category.xBEAUTY               1   2015.6 2095.6
## - category.xWEATHER              1   2015.8 2095.8
## - grupo_edades.x9.               1   2015.8 2095.8
## - ano_act.x2013                  1   2016.0 2096.0
## <none>                               2014.1 2096.1
## - category.xPHOTOGRAPHY          1   2016.5 2096.5
## - ano_act.x2016                  1   2016.8 2096.8
## - ano_act.x2017                  1   2017.1 2097.1
## - ano_act.x2014                  1   2017.3 2097.3
## - grupo_edades.x17.              1   2017.6 2097.6
## - category.xLIBRARIES_AND_DEMO   1   2018.6 2098.6
## - category.xEVENTS               1   2019.4 2099.4
## - category.xSHOPPING             1   2019.9 2099.9
## - grupo_edades.x4.               1   2020.0 2100.0
## - category.xDATING               1   2023.4 2103.4
## - category.xVIDEO_PLAYERS        1   2024.4 2104.4
## - category.xCOMICS               1   2025.9 2105.9
## - category.xTRAVEL_AND_LOCAL     1   2026.8 2106.8
## - category.xMAPS_AND_NAVIGATION  1   2028.3 2108.3
## - category.xHEALTH_AND_FITNESS   1   2028.6 2108.6
## - category.xPERSONALIZATION      1   2029.7 2109.7
## - category.xPRODUCTIVITY         1   2030.4 2110.4
## - category.xCOMMUNICATION        1   2031.2 2111.2
## - category.xTOOLS                1   2034.8 2114.8
## - category.xGAME                 1   2035.5 2115.5
## - category.xNEWS_AND_MAGAZINES   1   2036.9 2116.9
## - category.xBOOKS_AND_REFERENCE  1   2036.9 2116.9
## - category.xSOCIAL               1   2041.7 2121.7
## - category.xLIFESTYLE            1   2043.0 2123.0
## - category.xSPORTS               1   2045.3 2125.3
## - category.xFAMILY               1   2046.0 2126.0
## - category.xMEDICAL              1   2052.4 2132.4
## - rating_imp                     1   2053.6 2133.6
## - category.xBUSINESS             1   2057.0 2137.0
## - category.xFINANCE              1   2061.3 2141.3
## - type_bin                       1   2326.9 2406.9
## - reviews                        1   8344.1 8424.1
## 
## Step:  AIC=2094.78
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xBEAUTY + category.xBOOKS_AND_REFERENCE + category.xBUSINESS + 
##     category.xCOMICS + category.xCOMMUNICATION + category.xDATING + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2015 + ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## - ano_act.x2015                  1   2014.9 2092.9
## - ano_act.x2013                  1   2016.1 2094.1
## - android_ver_imp                1   2016.2 2094.2
## - category.xFOOD_AND_DRINK       1   2016.3 2094.3
## - category.xBEAUTY               1   2016.3 2094.3
## - category.xWEATHER              1   2016.5 2094.5
## - grupo_edades.x9.               1   2016.6 2094.6
## <none>                               2014.8 2094.8
## - category.xPHOTOGRAPHY          1   2017.2 2095.2
## - grupo_edades.x17.              1   2018.3 2096.3
## - ano_act.x2014                  1   2019.0 2097.0
## - category.xLIBRARIES_AND_DEMO   1   2019.4 2097.4
## - category.xEVENTS               1   2020.0 2098.0
## - category.xSHOPPING             1   2020.3 2098.3
## - grupo_edades.x4.               1   2020.8 2098.8
## - ano_act.x2016                  1   2021.3 2099.3
## - category.xDATING               1   2024.1 2102.1
## - category.xVIDEO_PLAYERS        1   2024.9 2102.9
## - category.xCOMICS               1   2026.5 2104.5
## - category.xTRAVEL_AND_LOCAL     1   2027.4 2105.4
## - category.xMAPS_AND_NAVIGATION  1   2028.9 2106.9
## - category.xHEALTH_AND_FITNESS   1   2029.1 2107.1
## - ano_act.x2017                  1   2029.3 2107.3
## - category.xPERSONALIZATION      1   2030.3 2108.3
## - category.xPRODUCTIVITY         1   2031.0 2109.0
## - category.xCOMMUNICATION        1   2031.7 2109.7
## - category.xTOOLS                1   2035.0 2113.0
## - category.xGAME                 1   2036.0 2114.0
## - category.xNEWS_AND_MAGAZINES   1   2037.5 2115.5
## - category.xBOOKS_AND_REFERENCE  1   2037.6 2115.6
## - category.xSOCIAL               1   2042.3 2120.3
## - category.xLIFESTYLE            1   2043.4 2121.4
## - category.xSPORTS               1   2045.9 2123.9
## - category.xFAMILY               1   2046.4 2124.4
## - category.xMEDICAL              1   2052.7 2130.7
## - rating_imp                     1   2054.4 2132.4
## - category.xBUSINESS             1   2057.3 2135.3
## - category.xFINANCE              1   2061.5 2139.5
## - type_bin                       1   2327.8 2405.8
## - reviews                        1   8345.0 8423.0
## 
## Step:  AIC=2092.86
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xBEAUTY + category.xBOOKS_AND_REFERENCE + category.xBUSINESS + 
##     category.xCOMICS + category.xCOMMUNICATION + category.xDATING + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2013 + ano_act.x2014 + 
##     ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## - ano_act.x2013                  1   2016.1 2092.1
## - android_ver_imp                1   2016.2 2092.2
## - category.xFOOD_AND_DRINK       1   2016.4 2092.4
## - category.xBEAUTY               1   2016.4 2092.4
## - category.xWEATHER              1   2016.6 2092.6
## - grupo_edades.x9.               1   2016.7 2092.7
## <none>                               2014.9 2092.9
## - category.xPHOTOGRAPHY          1   2017.3 2093.3
## - grupo_edades.x17.              1   2018.4 2094.4
## - ano_act.x2014                  1   2019.0 2095.0
## - category.xLIBRARIES_AND_DEMO   1   2019.5 2095.5
## - category.xEVENTS               1   2020.1 2096.1
## - category.xSHOPPING             1   2020.4 2096.4
## - grupo_edades.x4.               1   2020.9 2096.9
## - ano_act.x2016                  1   2021.3 2097.3
## - category.xDATING               1   2024.2 2100.2
## - category.xVIDEO_PLAYERS        1   2025.4 2101.4
## - category.xCOMICS               1   2026.6 2102.6
## - category.xTRAVEL_AND_LOCAL     1   2027.6 2103.6
## - category.xMAPS_AND_NAVIGATION  1   2029.1 2105.1
## - category.xHEALTH_AND_FITNESS   1   2029.4 2105.4
## - ano_act.x2017                  1   2029.5 2105.5
## - category.xPERSONALIZATION      1   2030.5 2106.5
## - category.xPRODUCTIVITY         1   2031.3 2107.3
## - category.xCOMMUNICATION        1   2032.0 2108.0
## - category.xTOOLS                1   2035.4 2111.4
## - category.xGAME                 1   2036.7 2112.7
## - category.xNEWS_AND_MAGAZINES   1   2037.7 2113.7
## - category.xBOOKS_AND_REFERENCE  1   2037.8 2113.8
## - category.xSOCIAL               1   2042.5 2118.5
## - category.xLIFESTYLE            1   2043.7 2119.7
## - category.xSPORTS               1   2046.1 2122.1
## - category.xFAMILY               1   2046.9 2122.9
## - category.xMEDICAL              1   2053.0 2129.0
## - rating_imp                     1   2054.4 2130.4
## - category.xBUSINESS             1   2057.7 2133.7
## - category.xFINANCE              1   2061.7 2137.7
## - type_bin                       1   2330.0 2406.0
## - reviews                        1   8399.3 8475.3
## 
## Step:  AIC=2092.1
## popular ~ reviews + type_bin + rating_imp + android_ver_imp + 
##     category.xBEAUTY + category.xBOOKS_AND_REFERENCE + category.xBUSINESS + 
##     category.xCOMICS + category.xCOMMUNICATION + category.xDATING + 
##     category.xEVENTS + category.xFAMILY + category.xFINANCE + 
##     category.xFOOD_AND_DRINK + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + 
##     ano_act.x2017
## 
##                                 Df Deviance    AIC
## - android_ver_imp                1   2016.9 2090.9
## - category.xFOOD_AND_DRINK       1   2017.6 2091.6
## - category.xBEAUTY               1   2017.6 2091.6
## - category.xWEATHER              1   2017.8 2091.8
## - grupo_edades.x9.               1   2018.0 2092.0
## <none>                               2016.1 2092.1
## - category.xPHOTOGRAPHY          1   2018.5 2092.5
## - grupo_edades.x17.              1   2019.7 2093.7
## - ano_act.x2014                  1   2019.8 2093.8
## - category.xLIBRARIES_AND_DEMO   1   2020.5 2094.5
## - category.xEVENTS               1   2021.3 2095.3
## - category.xSHOPPING             1   2021.6 2095.6
## - grupo_edades.x4.               1   2021.9 2095.9
## - ano_act.x2016                  1   2022.1 2096.1
## - category.xDATING               1   2025.6 2099.6
## - category.xVIDEO_PLAYERS        1   2027.1 2101.1
## - category.xCOMICS               1   2027.9 2101.9
## - category.xTRAVEL_AND_LOCAL     1   2028.8 2102.8
## - ano_act.x2017                  1   2030.1 2104.1
## - category.xMAPS_AND_NAVIGATION  1   2030.4 2104.4
## - category.xHEALTH_AND_FITNESS   1   2030.8 2104.8
## - category.xPERSONALIZATION      1   2032.6 2106.6
## - category.xPRODUCTIVITY         1   2032.7 2106.7
## - category.xCOMMUNICATION        1   2033.7 2107.7
## - category.xTOOLS                1   2036.9 2110.9
## - category.xGAME                 1   2038.2 2112.2
## - category.xBOOKS_AND_REFERENCE  1   2038.9 2112.9
## - category.xNEWS_AND_MAGAZINES   1   2038.9 2112.9
## - category.xSOCIAL               1   2043.9 2117.9
## - category.xLIFESTYLE            1   2045.2 2119.2
## - category.xSPORTS               1   2047.7 2121.7
## - category.xFAMILY               1   2048.0 2122.0
## - category.xMEDICAL              1   2054.7 2128.7
## - rating_imp                     1   2055.6 2129.6
## - category.xBUSINESS             1   2059.0 2133.0
## - category.xFINANCE              1   2063.2 2137.2
## - type_bin                       1   2331.9 2405.9
## - reviews                        1   8417.1 8491.1
## 
## Step:  AIC=2090.9
## popular ~ reviews + type_bin + rating_imp + category.xBEAUTY + 
##     category.xBOOKS_AND_REFERENCE + category.xBUSINESS + category.xCOMICS + 
##     category.xCOMMUNICATION + category.xDATING + category.xEVENTS + 
##     category.xFAMILY + category.xFINANCE + category.xFOOD_AND_DRINK + 
##     category.xGAME + category.xHEALTH_AND_FITNESS + category.xLIBRARIES_AND_DEMO + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + 
##     ano_act.x2017
## 
##                                 Df Deviance    AIC
## - category.xBEAUTY               1   2018.4 2090.4
## - category.xFOOD_AND_DRINK       1   2018.4 2090.4
## - category.xWEATHER              1   2018.6 2090.6
## - grupo_edades.x9.               1   2018.8 2090.8
## <none>                               2016.9 2090.9
## - category.xPHOTOGRAPHY          1   2019.3 2091.3
## - ano_act.x2014                  1   2020.0 2092.0
## - grupo_edades.x17.              1   2020.5 2092.5
## - category.xLIBRARIES_AND_DEMO   1   2020.8 2092.8
## - category.xEVENTS               1   2022.2 2094.2
## - category.xSHOPPING             1   2022.4 2094.4
## - ano_act.x2016                  1   2022.4 2094.4
## - grupo_edades.x4.               1   2022.7 2094.7
## - category.xDATING               1   2026.6 2098.6
## - category.xVIDEO_PLAYERS        1   2028.0 2100.0
## - category.xCOMICS               1   2028.8 2100.8
## - category.xTRAVEL_AND_LOCAL     1   2030.0 2102.0
## - ano_act.x2017                  1   2030.4 2102.4
## - category.xMAPS_AND_NAVIGATION  1   2031.4 2103.4
## - category.xHEALTH_AND_FITNESS   1   2032.0 2104.0
## - category.xPERSONALIZATION      1   2033.6 2105.6
## - category.xPRODUCTIVITY         1   2033.7 2105.7
## - category.xCOMMUNICATION        1   2034.3 2106.3
## - category.xTOOLS                1   2037.6 2109.6
## - category.xGAME                 1   2038.5 2110.5
## - category.xBOOKS_AND_REFERENCE  1   2039.4 2111.4
## - category.xNEWS_AND_MAGAZINES   1   2040.0 2112.0
## - category.xSOCIAL               1   2044.5 2116.5
## - category.xLIFESTYLE            1   2046.0 2118.0
## - category.xFAMILY               1   2048.6 2120.6
## - category.xSPORTS               1   2048.9 2120.9
## - category.xMEDICAL              1   2056.3 2128.3
## - rating_imp                     1   2056.5 2128.5
## - category.xBUSINESS             1   2060.2 2132.2
## - category.xFINANCE              1   2064.9 2136.9
## - type_bin                       1   2331.9 2403.9
## - reviews                        1   8417.2 8489.2
## 
## Step:  AIC=2090.38
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xFOOD_AND_DRINK + category.xGAME + 
##     category.xHEALTH_AND_FITNESS + category.xLIBRARIES_AND_DEMO + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + 
##     ano_act.x2017
## 
##                                 Df Deviance    AIC
## - category.xFOOD_AND_DRINK       1   2019.5 2089.5
## - category.xWEATHER              1   2019.9 2089.9
## - category.xPHOTOGRAPHY          1   2020.2 2090.2
## - grupo_edades.x9.               1   2020.2 2090.2
## <none>                               2018.4 2090.4
## - ano_act.x2014                  1   2021.4 2091.4
## - category.xLIBRARIES_AND_DEMO   1   2021.6 2091.6
## - grupo_edades.x17.              1   2021.9 2091.9
## - category.xEVENTS               1   2023.0 2093.0
## - category.xSHOPPING             1   2023.2 2093.2
## - ano_act.x2016                  1   2023.8 2093.8
## - grupo_edades.x4.               1   2024.4 2094.4
## - category.xDATING               1   2027.1 2097.1
## - category.xVIDEO_PLAYERS        1   2028.4 2098.4
## - category.xCOMICS               1   2029.4 2099.4
## - category.xTRAVEL_AND_LOCAL     1   2030.3 2100.3
## - ano_act.x2017                  1   2031.8 2101.8
## - category.xMAPS_AND_NAVIGATION  1   2031.8 2101.8
## - category.xHEALTH_AND_FITNESS   1   2032.2 2102.2
## - category.xPERSONALIZATION      1   2033.7 2103.7
## - category.xPRODUCTIVITY         1   2033.9 2103.9
## - category.xCOMMUNICATION        1   2034.4 2104.4
## - category.xTOOLS                1   2037.6 2107.6
## - category.xGAME                 1   2038.5 2108.5
## - category.xBOOKS_AND_REFERENCE  1   2039.6 2109.6
## - category.xNEWS_AND_MAGAZINES   1   2040.0 2110.0
## - category.xSOCIAL               1   2044.6 2114.6
## - category.xLIFESTYLE            1   2046.0 2116.0
## - category.xFAMILY               1   2048.9 2118.9
## - category.xSPORTS               1   2048.9 2118.9
## - category.xMEDICAL              1   2056.3 2126.3
## - rating_imp                     1   2058.4 2128.4
## - category.xBUSINESS             1   2060.3 2130.3
## - category.xFINANCE              1   2065.0 2135.0
## - type_bin                       1   2333.1 2403.1
## - reviews                        1   8429.9 8499.9
## 
## Step:  AIC=2089.47
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + category.xWEATHER + grupo_edades.x17. + 
##     grupo_edades.x4. + grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + 
##     ano_act.x2017
## 
##                                 Df Deviance    AIC
## - category.xWEATHER              1   2020.8 2088.8
## - category.xPHOTOGRAPHY          1   2020.9 2088.9
## - grupo_edades.x9.               1   2021.2 2089.2
## <none>                               2019.5 2089.5
## - category.xLIBRARIES_AND_DEMO   1   2022.1 2090.1
## - ano_act.x2014                  1   2022.5 2090.5
## - grupo_edades.x17.              1   2023.0 2091.0
## - category.xEVENTS               1   2023.5 2091.5
## - category.xSHOPPING             1   2023.6 2091.6
## - ano_act.x2016                  1   2024.9 2092.9
## - grupo_edades.x4.               1   2025.5 2093.5
## - category.xDATING               1   2027.5 2095.5
## - category.xVIDEO_PLAYERS        1   2028.6 2096.6
## - category.xCOMICS               1   2029.9 2097.9
## - category.xTRAVEL_AND_LOCAL     1   2030.4 2098.4
## - category.xMAPS_AND_NAVIGATION  1   2031.9 2099.9
## - category.xHEALTH_AND_FITNESS   1   2032.3 2100.3
## - ano_act.x2017                  1   2032.9 2100.9
## - category.xPERSONALIZATION      1   2033.7 2101.7
## - category.xPRODUCTIVITY         1   2033.9 2101.9
## - category.xCOMMUNICATION        1   2034.4 2102.4
## - category.xTOOLS                1   2037.7 2105.7
## - category.xGAME                 1   2038.6 2106.6
## - category.xBOOKS_AND_REFERENCE  1   2039.6 2107.6
## - category.xNEWS_AND_MAGAZINES   1   2040.0 2108.0
## - category.xSOCIAL               1   2044.6 2112.6
## - category.xLIFESTYLE            1   2046.1 2114.1
## - category.xSPORTS               1   2049.0 2117.0
## - category.xFAMILY               1   2049.9 2117.9
## - category.xMEDICAL              1   2056.6 2124.6
## - rating_imp                     1   2059.2 2127.2
## - category.xBUSINESS             1   2060.8 2128.8
## - category.xFINANCE              1   2065.4 2133.4
## - type_bin                       1   2334.2 2402.2
## - reviews                        1   8431.7 8499.7
## 
## Step:  AIC=2088.75
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPHOTOGRAPHY + category.xPRODUCTIVITY + category.xSHOPPING + 
##     category.xSOCIAL + category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## - category.xPHOTOGRAPHY          1   2021.9 2087.9
## - grupo_edades.x9.               1   2022.5 2088.5
## <none>                               2020.8 2088.8
## - category.xLIBRARIES_AND_DEMO   1   2023.2 2089.2
## - ano_act.x2014                  1   2024.0 2090.0
## - grupo_edades.x17.              1   2024.4 2090.4
## - category.xEVENTS               1   2024.5 2090.5
## - category.xSHOPPING             1   2024.6 2090.6
## - ano_act.x2016                  1   2026.2 2092.2
## - grupo_edades.x4.               1   2026.8 2092.8
## - category.xDATING               1   2028.5 2094.5
## - category.xVIDEO_PLAYERS        1   2029.5 2095.5
## - category.xCOMICS               1   2030.8 2096.8
## - category.xTRAVEL_AND_LOCAL     1   2031.1 2097.1
## - category.xMAPS_AND_NAVIGATION  1   2032.7 2098.7
## - category.xHEALTH_AND_FITNESS   1   2032.9 2098.9
## - ano_act.x2017                  1   2034.3 2100.3
## - category.xPERSONALIZATION      1   2034.3 2100.3
## - category.xPRODUCTIVITY         1   2034.4 2100.4
## - category.xCOMMUNICATION        1   2035.0 2101.0
## - category.xTOOLS                1   2038.0 2104.0
## - category.xGAME                 1   2038.9 2104.9
## - category.xBOOKS_AND_REFERENCE  1   2040.2 2106.2
## - category.xNEWS_AND_MAGAZINES   1   2040.5 2106.5
## - category.xSOCIAL               1   2045.2 2111.2
## - category.xLIFESTYLE            1   2046.4 2112.4
## - category.xSPORTS               1   2049.3 2115.3
## - category.xFAMILY               1   2050.0 2116.0
## - category.xMEDICAL              1   2056.8 2122.8
## - rating_imp                     1   2060.4 2126.4
## - category.xBUSINESS             1   2061.0 2127.0
## - category.xFINANCE              1   2065.6 2131.6
## - type_bin                       1   2335.2 2401.2
## - reviews                        1   8439.4 8505.4
## 
## Step:  AIC=2087.93
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSHOPPING + category.xSOCIAL + 
##     category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + grupo_edades.x17. + grupo_edades.x4. + 
##     grupo_edades.x9. + ano_act.x2014 + ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## - grupo_edades.x9.               1   2023.7 2087.7
## - category.xLIBRARIES_AND_DEMO   1   2023.9 2087.9
## <none>                               2021.9 2087.9
## - category.xEVENTS               1   2025.2 2089.2
## - category.xSHOPPING             1   2025.2 2089.2
## - ano_act.x2014                  1   2025.3 2089.3
## - grupo_edades.x17.              1   2025.6 2089.6
## - ano_act.x2016                  1   2027.6 2091.6
## - grupo_edades.x4.               1   2027.9 2091.9
## - category.xDATING               1   2029.1 2093.1
## - category.xVIDEO_PLAYERS        1   2029.8 2093.8
## - category.xTRAVEL_AND_LOCAL     1   2031.3 2095.3
## - category.xCOMICS               1   2031.4 2095.4
## - category.xMAPS_AND_NAVIGATION  1   2033.0 2097.0
## - category.xHEALTH_AND_FITNESS   1   2033.0 2097.0
## - category.xPERSONALIZATION      1   2034.4 2098.4
## - category.xPRODUCTIVITY         1   2034.5 2098.5
## - category.xCOMMUNICATION        1   2035.1 2099.1
## - ano_act.x2017                  1   2036.2 2100.2
## - category.xTOOLS                1   2038.0 2102.0
## - category.xGAME                 1   2039.0 2103.0
## - category.xBOOKS_AND_REFERENCE  1   2040.3 2104.3
## - category.xNEWS_AND_MAGAZINES   1   2040.6 2104.6
## - category.xSOCIAL               1   2045.3 2109.3
## - category.xLIFESTYLE            1   2046.5 2110.5
## - category.xSPORTS               1   2049.3 2113.3
## - category.xFAMILY               1   2050.7 2114.7
## - category.xMEDICAL              1   2057.0 2121.0
## - rating_imp                     1   2061.0 2125.0
## - category.xBUSINESS             1   2061.3 2125.3
## - category.xFINANCE              1   2065.8 2129.8
## - type_bin                       1   2338.3 2402.3
## - reviews                        1   8449.6 8513.6
## 
## Step:  AIC=2087.7
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIBRARIES_AND_DEMO + category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + 
##     category.xMEDICAL + category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSHOPPING + category.xSOCIAL + 
##     category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + grupo_edades.x17. + grupo_edades.x4. + 
##     ano_act.x2014 + ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## - category.xLIBRARIES_AND_DEMO   1   2025.6 2087.6
## <none>                               2023.7 2087.7
## - grupo_edades.x17.              1   2026.5 2088.5
## - category.xEVENTS               1   2026.9 2088.9
## - ano_act.x2014                  1   2027.0 2089.0
## - category.xSHOPPING             1   2027.0 2089.0
## - grupo_edades.x4.               1   2027.9 2089.9
## - ano_act.x2016                  1   2029.6 2091.6
## - category.xDATING               1   2031.0 2093.0
## - category.xVIDEO_PLAYERS        1   2031.4 2093.4
## - category.xTRAVEL_AND_LOCAL     1   2033.0 2095.0
## - category.xCOMICS               1   2033.5 2095.5
## - category.xHEALTH_AND_FITNESS   1   2034.7 2096.7
## - category.xMAPS_AND_NAVIGATION  1   2034.7 2096.7
## - category.xPRODUCTIVITY         1   2036.2 2098.2
## - category.xPERSONALIZATION      1   2036.4 2098.4
## - category.xCOMMUNICATION        1   2037.0 2099.0
## - ano_act.x2017                  1   2038.2 2100.2
## - category.xTOOLS                1   2039.6 2101.6
## - category.xGAME                 1   2041.3 2103.3
## - category.xNEWS_AND_MAGAZINES   1   2041.4 2103.4
## - category.xBOOKS_AND_REFERENCE  1   2041.8 2103.8
## - category.xLIFESTYLE            1   2047.9 2109.9
## - category.xSOCIAL               1   2048.5 2110.5
## - category.xSPORTS               1   2050.9 2112.9
## - category.xFAMILY               1   2052.4 2114.4
## - category.xMEDICAL              1   2058.4 2120.4
## - rating_imp                     1   2062.7 2124.7
## - category.xBUSINESS             1   2063.1 2125.1
## - category.xFINANCE              1   2067.4 2129.4
## - type_bin                       1   2338.3 2400.3
## - reviews                        1   8467.7 8529.7
## 
## Step:  AIC=2087.63
## popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSHOPPING + category.xSOCIAL + 
##     category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + grupo_edades.x17. + grupo_edades.x4. + 
##     ano_act.x2014 + ano_act.x2016 + ano_act.x2017
## 
##                                 Df Deviance    AIC
## <none>                               2025.6 2087.6
## - category.xEVENTS               1   2028.3 2088.3
## - category.xSHOPPING             1   2028.4 2088.4
## - grupo_edades.x17.              1   2028.5 2088.5
## - ano_act.x2014                  1   2028.8 2088.8
## - grupo_edades.x4.               1   2029.7 2089.7
## - ano_act.x2016                  1   2031.4 2091.4
## - category.xDATING               1   2032.4 2092.4
## - category.xVIDEO_PLAYERS        1   2032.5 2092.5
## - category.xTRAVEL_AND_LOCAL     1   2033.9 2093.9
## - category.xCOMICS               1   2034.9 2094.9
## - category.xHEALTH_AND_FITNESS   1   2035.5 2095.5
## - category.xMAPS_AND_NAVIGATION  1   2035.7 2095.7
## - category.xPRODUCTIVITY         1   2036.9 2096.9
## - category.xPERSONALIZATION      1   2037.2 2097.2
## - category.xCOMMUNICATION        1   2037.7 2097.7
## - category.xTOOLS                1   2039.9 2099.9
## - ano_act.x2017                  1   2041.2 2101.2
## - category.xGAME                 1   2041.7 2101.7
## - category.xNEWS_AND_MAGAZINES   1   2042.0 2102.0
## - category.xBOOKS_AND_REFERENCE  1   2042.6 2102.6
## - category.xLIFESTYLE            1   2048.1 2108.1
## - category.xSOCIAL               1   2049.2 2109.2
## - category.xSPORTS               1   2051.3 2111.3
## - category.xFAMILY               1   2052.4 2112.4
## - category.xMEDICAL              1   2058.5 2118.5
## - category.xBUSINESS             1   2063.1 2123.1
## - rating_imp                     1   2065.0 2125.0
## - category.xFINANCE              1   2067.5 2127.5
## - type_bin                       1   2339.4 2399.4
## - reviews                        1   8485.9 8545.9

summary(model_2)

## 
## Call:
## glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xDATING + category.xEVENTS + category.xFAMILY + 
##     category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSHOPPING + category.xSOCIAL + 
##     category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
##     category.xVIDEO_PLAYERS + grupo_edades.x17. + grupo_edades.x4. + 
##     ano_act.x2014 + ano_act.x2016 + ano_act.x2017, family = "binomial", 
##     data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -4.9596  -0.2980   0.0008   0.0014   3.5644  
## 
## Coefficients:
##                                 Estimate Std. Error z value
## (Intercept)                    0.3256196  0.4434563   0.734
## reviews                        0.0025651  0.0001013  25.327
## type_bin                      -8.1454415  0.6692997 -12.170
## rating_imp                    -0.5584931  0.0863395  -6.469
## category.xBOOKS_AND_REFERENCE -1.8691146  0.5150485  -3.629
## category.xBUSINESS            -1.8937094  0.3577243  -5.294
## category.xCOMICS              -2.2917798  0.8529493  -2.687
## category.xCOMMUNICATION       -1.2415271  0.3864343  -3.213
## category.xDATING              -1.4075128  0.5492249  -2.563
## category.xEVENTS              -0.8455897  0.5501968  -1.537
## category.xFAMILY              -0.9795207  0.1891670  -5.178
## category.xFINANCE             -2.2607102  0.4142731  -5.457
## category.xGAME                -1.1327329  0.2948277  -3.842
## category.xHEALTH_AND_FITNESS  -1.1060827  0.3787786  -2.920
## category.xLIFESTYLE           -1.4094100  0.3202885  -4.400
## category.xMAPS_AND_NAVIGATION -1.5309902  0.5450130  -2.809
## category.xMEDICAL             -1.8111919  0.3584871  -5.052
## category.xNEWS_AND_MAGAZINES  -1.4965058  0.4085322  -3.663
## category.xPERSONALIZATION     -1.1838232  0.3758839  -3.149
## category.xPRODUCTIVITY        -1.1110392  0.3546183  -3.133
## category.xSHOPPING            -0.7558444  0.4820156  -1.568
## category.xSOCIAL              -2.4638362  0.5980034  -4.120
## category.xSPORTS              -1.8203606  0.3865600  -4.709
## category.xTOOLS               -0.8327901  0.2240891  -3.716
## category.xTRAVEL_AND_LOCAL    -1.0944288  0.4098848  -2.670
## category.xVIDEO_PLAYERS       -1.1553295  0.4685611  -2.466
## grupo_edades.x17.              0.8384517  0.4880515   1.718
## grupo_edades.x4.               0.4528372  0.2300680   1.968
## ano_act.x2014                 -0.6664322  0.3882616  -1.716
## ano_act.x2016                 -0.5307236  0.2291425  -2.316
## ano_act.x2017                 -0.5889548  0.1538303  -3.829
##                                           Pr(>|z|)    
## (Intercept)                               0.462780    
## reviews                       < 0.0000000000000002 ***
## type_bin                      < 0.0000000000000002 ***
## rating_imp                         0.0000000000989 ***
## category.xBOOKS_AND_REFERENCE             0.000285 ***
## category.xBUSINESS                 0.0000001198211 ***
## category.xCOMICS                          0.007212 ** 
## category.xCOMMUNICATION                   0.001315 ** 
## category.xDATING                          0.010385 *  
## category.xEVENTS                          0.124321    
## category.xFAMILY                   0.0000002241897 ***
## category.xFINANCE                  0.0000000484104 ***
## category.xGAME                            0.000122 ***
## category.xHEALTH_AND_FITNESS              0.003499 ** 
## category.xLIFESTYLE                0.0000108031699 ***
## category.xMAPS_AND_NAVIGATION             0.004968 ** 
## category.xMEDICAL                  0.0000004364725 ***
## category.xNEWS_AND_MAGAZINES              0.000249 ***
## category.xPERSONALIZATION                 0.001636 ** 
## category.xPRODUCTIVITY                    0.001730 ** 
## category.xSHOPPING                        0.116860    
## category.xSOCIAL                   0.0000378701585 ***
## category.xSPORTS                   0.0000024877917 ***
## category.xTOOLS                           0.000202 ***
## category.xTRAVEL_AND_LOCAL                0.007583 ** 
## category.xVIDEO_PLAYERS                   0.013675 *  
## grupo_edades.x17.                         0.085804 .  
## grupo_edades.x4.                          0.049036 *  
## ano_act.x2014                             0.086079 .  
## ano_act.x2016                             0.020551 *  
## ano_act.x2017                             0.000129 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9975.4  on 7248  degrees of freedom
## Residual deviance: 2025.6  on 7218  degrees of freedom
## AIC: 2087.6
## 
## Number of Fisher Scoring iterations: 9

Las variables con el coeficiente el p-valor más alto son type_bin, reviews, category.xBOOKS_AND_REFERENCE, category.xBUSINESS, category.xCOMICS, category.xFINANCE, category.xSPORTS, category.xVIDEO_PLAYERS y category.xSOCIAL. Al mismo tiempo, category.xSHOPPING, category.xEVENTS, grupo_edades.x17 y ano_act.x2014 no son estadísticamente significativas por lo que podrían eliminarse del análisis.

Se utilizará el factor de inflación de la varianza (vif) para eliminar los predictores redundantes o las variables que tienen una alta multicolinealidad entre ellos. El VIF mide la cantidad de varianza de una variable que se puede explicar por otras variables en el modelo. Un VIF de 1 indica que la variable no está correlacionada con otras variables en el modelo, mientras que un VIF superior a 1 indica que la variable está correlacionada con otras variables en el modelo.

car::vif(model_2)

##                       reviews                      type_bin 
##                      1.590630                      1.473004 
##                    rating_imp category.xBOOKS_AND_REFERENCE 
##                      1.076671                      1.077197 
##            category.xBUSINESS              category.xCOMICS 
##                      1.144185                      1.049969 
##       category.xCOMMUNICATION              category.xDATING 
##                      1.128051                      2.705575 
##              category.xEVENTS              category.xFAMILY 
##                      1.059053                      1.771376 
##             category.xFINANCE                category.xGAME 
##                      1.115258                      1.359045 
##  category.xHEALTH_AND_FITNESS           category.xLIFESTYLE 
##                      1.132575                      1.195243 
## category.xMAPS_AND_NAVIGATION             category.xMEDICAL 
##                      1.060665                      1.146465 
##  category.xNEWS_AND_MAGAZINES     category.xPERSONALIZATION 
##                      1.111806                      1.150098 
##        category.xPRODUCTIVITY            category.xSHOPPING 
##                      1.147852                      1.073984 
##              category.xSOCIAL              category.xSPORTS 
##                      1.096141                      1.152683 
##               category.xTOOLS    category.xTRAVEL_AND_LOCAL 
##                      1.487034                      1.115659 
##       category.xVIDEO_PLAYERS             grupo_edades.x17. 
##                      1.087282                      3.034021 
##              grupo_edades.x4.                 ano_act.x2014 
##                      1.719947                      1.046145 
##                 ano_act.x2016                 ano_act.x2017 
##                      1.038117                      1.040019

Se observa que la mayoría de las variables tienen un VIF entre 1 y 2, lo que sugiere que no hay una multicolinealidad importante presente en el modelo. De esta manera, “un predictor que tiene un VIF de 2 o menos generalmente se considera seguro y se puede suponer que no está correlacionado con otras variables predictoras”.

3.1.1.3 Modelo 3

Se aplicará el modelo_2 sin las variables sin significancia estadística del modelo_2 (category.xSHOPPING, category.xEVENTS, grupo_edades.x17 y ano_act.x2014)

model_3 <- glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
    category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION  + category.xFAMILY + 
    category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
    category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
    category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
    category.xPRODUCTIVITY  + category.xSOCIAL + 
    category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
    category.xVIDEO_PLAYERS  + ano_act.x2016 + ano_act.x2017 + category.xDATING + grupo_edades.x4., family = "binomial", data = train)
summary(model_3)

## 
## Call:
## glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xFAMILY + category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     ano_act.x2016 + ano_act.x2017 + category.xDATING + grupo_edades.x4., 
##     family = "binomial", data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -4.9751  -0.2980   0.0007   0.0014   3.6067  
## 
## Coefficients:
##                                 Estimate Std. Error z value
## (Intercept)                    0.3485971  0.4262971   0.818
## reviews                        0.0025602  0.0001007  25.430
## type_bin                      -8.1446070  0.6686982 -12.180
## rating_imp                    -0.5617996  0.0858054  -6.547
## category.xBOOKS_AND_REFERENCE -1.7550526  0.5092750  -3.446
## category.xBUSINESS            -1.7855512  0.3553920  -5.024
## category.xCOMICS              -2.1214243  0.8690952  -2.441
## category.xCOMMUNICATION       -1.1165792  0.3827254  -2.917
## category.xFAMILY              -0.8625122  0.1809668  -4.766
## category.xFINANCE             -2.1159912  0.4099957  -5.161
## category.xGAME                -1.0672780  0.2885420  -3.699
## category.xHEALTH_AND_FITNESS  -0.9741456  0.3750889  -2.597
## category.xLIFESTYLE           -1.2788397  0.3153649  -4.055
## category.xMAPS_AND_NAVIGATION -1.3891143  0.5418198  -2.564
## category.xMEDICAL             -1.6758247  0.3538254  -4.736
## category.xNEWS_AND_MAGAZINES  -1.3960021  0.4058702  -3.440
## category.xPERSONALIZATION     -1.1119307  0.3718230  -2.990
## category.xPRODUCTIVITY        -0.9934965  0.3492538  -2.845
## category.xSOCIAL              -2.3615727  0.5976708  -3.951
## category.xSPORTS              -1.6807647  0.3820530  -4.399
## category.xTOOLS               -0.7128830  0.2171869  -3.282
## category.xTRAVEL_AND_LOCAL    -0.9554333  0.4060406  -2.353
## category.xVIDEO_PLAYERS       -1.0451383  0.4699643  -2.224
## ano_act.x2016                 -0.5075043  0.2282188  -2.224
## ano_act.x2017                 -0.5687543  0.1527835  -3.723
## category.xDATING              -0.6378535  0.3919167  -1.628
## grupo_edades.x4.               0.2986621  0.2082569   1.434
##                                           Pr(>|z|)    
## (Intercept)                               0.413510    
## reviews                       < 0.0000000000000002 ***
## type_bin                      < 0.0000000000000002 ***
## rating_imp                         0.0000000000586 ***
## category.xBOOKS_AND_REFERENCE             0.000569 ***
## category.xBUSINESS                 0.0000005056043 ***
## category.xCOMICS                          0.014648 *  
## category.xCOMMUNICATION                   0.003529 ** 
## category.xFAMILY                   0.0000018779244 ***
## category.xFINANCE                  0.0000002456230 ***
## category.xGAME                            0.000217 ***
## category.xHEALTH_AND_FITNESS              0.009401 ** 
## category.xLIFESTYLE                0.0000501104418 ***
## category.xMAPS_AND_NAVIGATION             0.010354 *  
## category.xMEDICAL                  0.0000021765121 ***
## category.xNEWS_AND_MAGAZINES              0.000583 ***
## category.xPERSONALIZATION                 0.002785 ** 
## category.xPRODUCTIVITY                    0.004446 ** 
## category.xSOCIAL                   0.0000777298835 ***
## category.xSPORTS                   0.0000108601821 ***
## category.xTOOLS                           0.001029 ** 
## category.xTRAVEL_AND_LOCAL                0.018620 *  
## category.xVIDEO_PLAYERS                   0.026157 *  
## ano_act.x2016                             0.026164 *  
## ano_act.x2017                             0.000197 ***
## category.xDATING                          0.103626    
## grupo_edades.x4.                          0.151542    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9975.4  on 7248  degrees of freedom
## Residual deviance: 2036.7  on 7222  degrees of freedom
## AIC: 2090.7
## 
## Number of Fisher Scoring iterations: 9

car::vif(model_3)

##                       reviews                      type_bin 
##                      1.569844                      1.462363 
##                    rating_imp category.xBOOKS_AND_REFERENCE 
##                      1.072786                      1.066314 
##            category.xBUSINESS              category.xCOMICS 
##                      1.116923                      1.040181 
##       category.xCOMMUNICATION              category.xFAMILY 
##                      1.101597                      1.626308 
##             category.xFINANCE                category.xGAME 
##                      1.095646                      1.303909 
##  category.xHEALTH_AND_FITNESS           category.xLIFESTYLE 
##                      1.109061                      1.160791 
## category.xMAPS_AND_NAVIGATION             category.xMEDICAL 
##                      1.050052                      1.121012 
##  category.xNEWS_AND_MAGAZINES     category.xPERSONALIZATION 
##                      1.091261                      1.110079 
##        category.xPRODUCTIVITY              category.xSOCIAL 
##                      1.122120                      1.082080 
##              category.xSPORTS               category.xTOOLS 
##                      1.128971                      1.404621 
##    category.xTRAVEL_AND_LOCAL       category.xVIDEO_PLAYERS 
##                      1.096217                      1.070644 
##                 ano_act.x2016                 ano_act.x2017 
##                      1.033930                      1.031542 
##              category.xDATING              grupo_edades.x4. 
##                      1.419840                      1.421911

Respecto a los vectores de inflación todas las variables se encuentran entre 1 y 2. Se observa que category.xDATING y grupo_edades.x4. no tienen significancia estadística para un nivel de significancia del 5% por lo que se realizará un modelo_4 sin estas variables:

model_4 <- glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
    category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION  + category.xFAMILY + 
    category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
    category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
    category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
    category.xPRODUCTIVITY  + category.xSOCIAL + 
    category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
    category.xVIDEO_PLAYERS  + ano_act.x2016 + ano_act.x2017, family = "binomial", data = train)

summary(model_4)

## 
## Call:
## glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
##     category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION + 
##     category.xFAMILY + category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
##     category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
##     category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
##     category.xPRODUCTIVITY + category.xSOCIAL + category.xSPORTS + 
##     category.xTOOLS + category.xTRAVEL_AND_LOCAL + category.xVIDEO_PLAYERS + 
##     ano_act.x2016 + ano_act.x2017, family = "binomial", data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -4.9794  -0.3035   0.0008   0.0014   3.6311  
## 
## Coefficients:
##                                  Estimate  Std. Error z value
## (Intercept)                    0.45072109  0.36798100   1.225
## reviews                        0.00253901  0.00009965  25.480
## type_bin                      -8.06055102  0.66402834 -12.139
## rating_imp                    -0.55001164  0.08574821  -6.414
## category.xBOOKS_AND_REFERENCE -1.59813146  0.50349542  -3.174
## category.xBUSINESS            -1.63688534  0.35066341  -4.668
## category.xCOMICS              -2.12291787  0.86278911  -2.461
## category.xCOMMUNICATION       -0.99406376  0.37766591  -2.632
## category.xFAMILY              -0.75282151  0.17367632  -4.335
## category.xFINANCE             -1.95395604  0.40534114  -4.821
## category.xGAME                -1.03269695  0.27715374  -3.726
## category.xHEALTH_AND_FITNESS  -0.84029891  0.37051717  -2.268
## category.xLIFESTYLE           -1.14046646  0.31063321  -3.671
## category.xMAPS_AND_NAVIGATION -1.22974715  0.53798234  -2.286
## category.xMEDICAL             -1.52807807  0.34863293  -4.383
## category.xNEWS_AND_MAGAZINES  -1.27051095  0.40092525  -3.169
## category.xPERSONALIZATION     -1.00878194  0.36541431  -2.761
## category.xPRODUCTIVITY        -0.84578015  0.34440360  -2.456
## category.xSOCIAL              -2.35734537  0.58468320  -4.032
## category.xSPORTS              -1.52817639  0.37714788  -4.052
## category.xTOOLS               -0.56057817  0.21130254  -2.653
## category.xTRAVEL_AND_LOCAL    -0.79787140  0.40208337  -1.984
## category.xVIDEO_PLAYERS       -0.91554861  0.46683842  -1.961
## ano_act.x2016                 -0.50852983  0.22868184  -2.224
## ano_act.x2017                 -0.55067071  0.15299143  -3.599
##                                           Pr(>|z|)    
## (Intercept)                               0.220632    
## reviews                       < 0.0000000000000002 ***
## type_bin                      < 0.0000000000000002 ***
## rating_imp                          0.000000000142 ***
## category.xBOOKS_AND_REFERENCE             0.001503 ** 
## category.xBUSINESS                  0.000003041942 ***
## category.xCOMICS                          0.013873 *  
## category.xCOMMUNICATION                   0.008485 ** 
## category.xFAMILY                    0.000014600969 ***
## category.xFINANCE                   0.000001431828 ***
## category.xGAME                            0.000194 ***
## category.xHEALTH_AND_FITNESS              0.023335 *  
## category.xLIFESTYLE                       0.000241 ***
## category.xMAPS_AND_NAVIGATION             0.022263 *  
## category.xMEDICAL                   0.000011702537 ***
## category.xNEWS_AND_MAGAZINES              0.001530 ** 
## category.xPERSONALIZATION                 0.005769 ** 
## category.xPRODUCTIVITY                    0.014058 *  
## category.xSOCIAL                    0.000055343373 ***
## category.xSPORTS                    0.000050797096 ***
## category.xTOOLS                           0.007979 ** 
## category.xTRAVEL_AND_LOCAL                0.047218 *  
## category.xVIDEO_PLAYERS                   0.049859 *  
## ano_act.x2016                             0.026166 *  
## ano_act.x2017                             0.000319 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9975.4  on 7248  degrees of freedom
## Residual deviance: 2045.8  on 7224  degrees of freedom
## AIC: 2095.8
## 
## Number of Fisher Scoring iterations: 9

car::vif(model_4)

##                       reviews                      type_bin 
##                      1.551758                      1.458784 
##                    rating_imp category.xBOOKS_AND_REFERENCE 
##                      1.066679                      1.056401 
##            category.xBUSINESS              category.xCOMICS 
##                      1.096669                      1.023141 
##       category.xCOMMUNICATION              category.xFAMILY 
##                      1.084677                      1.503305 
##             category.xFINANCE                category.xGAME 
##                      1.078281                      1.186952 
##  category.xHEALTH_AND_FITNESS           category.xLIFESTYLE 
##                      1.090422                      1.133291 
## category.xMAPS_AND_NAVIGATION             category.xMEDICAL 
##                      1.041032                      1.100225 
##  category.xNEWS_AND_MAGAZINES     category.xPERSONALIZATION 
##                      1.075506                      1.090835 
##        category.xPRODUCTIVITY              category.xSOCIAL 
##                      1.101478                      1.047189 
##              category.xSPORTS               category.xTOOLS 
##                      1.108778                      1.334461 
##    category.xTRAVEL_AND_LOCAL       category.xVIDEO_PLAYERS 
##                      1.079966                      1.059048 
##                 ano_act.x2016                 ano_act.x2017 
##                      1.034841                      1.030511

Todas las variables tienen significancia estadística en este último modelo

# Obtener los residuos
residuos <- residuals(model_4, type = "deviance")
summary(residuos)

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -4.979407 -0.303497  0.000814 -0.067982  0.001425  3.631136

par(mfrow=c(1, 2))

plot(model_3, main="Modelo 3", pch=19, cex=1, which=1)
plot(model_4, main="Modelo 4", pch=19, cex=1, which=1)

Se puede observar que la media de los residuos es cercana a cero, lo que indica que el modelo tiene un buen ajuste en términos generales. Al mismo tiempo, hay valores extremos en los residuos, lo que puede indicar la presencia de valores atípicos o errores en el modelo. Se elegirá el modelo_4 como modelo final.

Analizamos los Odds Ratio

final_model <- model_4

#calculamos los ods ratio
exp(coef(final_model))

##                   (Intercept)                       reviews 
##                  1.5694434851                  1.0025422378 
##                      type_bin                    rating_imp 
##                  0.0003157528                  0.5769430973 
## category.xBOOKS_AND_REFERENCE            category.xBUSINESS 
##                  0.2022741231                  0.1945851651 
##              category.xCOMICS       category.xCOMMUNICATION 
##                  0.1196819025                  0.3700697550 
##              category.xFAMILY             category.xFINANCE 
##                  0.4710356464                  0.1417123418 
##                category.xGAME  category.xHEALTH_AND_FITNESS 
##                  0.3560454261                  0.4315815011 
##           category.xLIFESTYLE category.xMAPS_AND_NAVIGATION 
##                  0.3196698728                  0.2923664933 
##             category.xMEDICAL  category.xNEWS_AND_MAGAZINES 
##                  0.2169522344                  0.2806881688 
##     category.xPERSONALIZATION        category.xPRODUCTIVITY 
##                  0.3646628897                  0.4292223715 
##              category.xSOCIAL              category.xSPORTS 
##                  0.0946712066                  0.2169309039 
##               category.xTOOLS    category.xTRAVEL_AND_LOCAL 
##                  0.5708789048                  0.4502864237 
##       category.xVIDEO_PLAYERS                 ano_act.x2016 
##                  0.4002969596                  0.6013790566 
##                 ano_act.x2017 
##                  0.5765629750

El Odd Ratio indica cuántas veces más probable es que ocurra un evento dado (que la app sea popular), cuando se compara un cambio en una unidad de la variable popular.

3.1.1.4 Evaluación del modelo

pred <- predict(final_model, type = "response", newdata = validation)
summary(pred)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.000004 0.057112 0.761552 0.549189 0.999999 1.000000

validation$prob <- pred

# Using probability cutoff of 50%.

pred_popular <- factor(ifelse(pred >= 0.50, "Yes", "No"))
actual_popular <- factor(ifelse(validation$popular==1,"Yes","No"))
table(actual_popular,pred_popular)

##               pred_popular
## actual_popular   No  Yes
##            No  1361   36
##            Yes  129 1581

Vamos a calcular la sensibilidad, la especificidad y accuracy con un corte de 0.50

cutoff_popular <- factor(ifelse(pred >=0.50, "Yes", "No"))
conf_final <- confusionMatrix(cutoff_popular, actual_popular, positive = "Yes")
accuracy <- conf_final$overall[1]
sensitivity <- conf_final$byClass[1]
specificity <- conf_final$byClass[2]
accuracy

##  Accuracy 
## 0.9468941

sensitivity

## Sensitivity 
##   0.9245614

specificity

## Specificity 
##   0.9742305

La sensibilidad nos indica la capacidad de nuestro estimador para dar como casos positivos. En este caso, nuestro modelo tiene una sensibilidad de 0.92. La especificidad nos indica la capacidad de nuestro estimador para dar como casos negativos, el model_4 posee un nivel de especificidad de 0.97, y, por último, Accuracy es lo que mide en base a la diagonal cuantos de las apps populares reales (0.94).

perform_app <- function(cutoff) 
{
  predicted_popular <- factor(ifelse(pred >= cutoff, "Yes", "No"))
  conf <- confusionMatrix(predicted_popular, actual_popular, positive = "Yes")
  accuray <- conf$overall[1]
  sensitivity <- conf$byClass[1]
  specificity <- conf$byClass[2]
  out <- t(as.matrix(c(sensitivity, specificity, accuray))) 
  colnames(out) <- c("sensitivity", "specificity", "accuracy")
  return(out)
}


options(repr.plot.width =8, repr.plot.height =6)
summary(pred)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.000004 0.057112 0.761552 0.549189 0.999999 1.000000

s = seq(0.01,0.80,length=100)
OUT = matrix(0,100,3)

for(i in 1:100)
{
  OUT[i,] = perform_app(s[i])
} 

plot(s, OUT[,1],xlab="Cutoff",ylab="Value",cex.lab=1.5,cex.axis=1.5,ylim=c(0,1),
     type="l",lwd=2,axes=FALSE,col=2)
axis(1,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.5)
axis(2,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.5)
lines(s,OUT[,2],col="darkgreen",lwd=2)
lines(s,OUT[,3],col=4,lwd=2)
box()
legend("bottom",col=c(2,"darkgreen",4,"darkred"),text.font =3,inset = 0.02,
       box.lty=0,cex = 0.8, 
       lwd=c(2,2,2,2),c("Sensitivity","Specificity","Accuracy"))
abline(v = 0.32, col="red", lwd=1, lty=2)
axis(1, at = seq(0.1, 1, by = 0.1))

#cutoff <- s[which(abs(OUT[,1]-OUT[,2])<0.01)]

Según los resultados, el modelo es es capaz de predecir correctamente el 94.9% de los casos.

---
title: "Trabajo Final - Estadística Aplicada a la Investigación de Mercado"
author: "Ariana Bard"
output: 
  html_document:
    code_download: true
    toc: TRUE
    toc_float: TRUE
    css: hoja_estilo_tp.css
    number_sections: true
    theme: "flatly"
    highlight: textmate
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning =FALSE,message = FALSE)

#EDA
library(tidyverse)
library(readr)
library(janitor)
library(gt)
library(plotly)
library(RColorBrewer)
library(gridExtra)
library(lubridate)
library(kableExtra)
library(skimr)
library(robustHD)
library(data.table)


#valores nulos
library(naniar)
library(mice)
library(visdat)

#para el grafico waffle
library(waffle)

#Arbol de decisión
library(rpart)
library(rpart.plot)
library(rattle)

# curva ROC
library(pROC)
library(caret)


#evitar la notación científica
options(scipen=999)
```

El objetivo de este trabajo final es utilizar DOS técnicas de las que se
vieron durante la materia **Estadística Aplicada a la Investigación de
Mercado.**

# Aplicaciones de Google Play Store

La base de datos fue extraida de kaggle[^1], se trata de un dataset
público construido a partir de webscrapping con el objetivo de analizar
el mercado de las aplicaciones de android. La misma fue publicada hace 4
años por Lavanya Gupta.

[^1]: <https://www.kaggle.com/datasets/lava18/google-play-store-apps>

**Las variables que posee el dataframe son las siguientes**. Es
importante resaltar que toda esta información es de cuando fue
escrapeada la base. Es decir en 2019.

| Variable          | Descripción                                                                 |
|----------------------|--------------------------------------------------|
| `Apps`            | Nombre de la aplicación                                                     |
| `Category`        | Categoría a la que pertenece la app                                         |
| `Rating`          | Puntaje que los usuarios le dieron a la app                                 |
| `Reviews`         | Cantidad de comentarios de la app                                           |
| `Size`            | Tamaño de la app                                                            |
| `Installs`        | Cantidad de usuarios que descargaron la app                                 |
| `Type`            | Si es paga (paid) o gratuita (free)                                         |
| `Price`           | Precio de la app                                                            |
| `Content Raiting` | Grupo de edad para la cual es la app (Children/Mature +21/ Adult /Everyone) |
| `Genres`          | Genero de la App. Una App puede pertenecer a multiples generos              |
| `Last Updated`    | Fecha de la última actualización                                            |
| `Current Ver`     | Versión actual de la aplicación que se encuentra disponible en playstore    |
| `Android Ver`     | Versión mínima de android necesaria para descargar la app                   |

: Variables y descripción

**La Asociación por el Derecho al Acceso (ADA)** quiere desarrollar una
aplicación de Google Playstore que sirva para promocionar y difundir el
derecho al acceso a la información, por eso necesitan conocer el mercado
de aplicaciones de Google Playstore

El **objetivo** de este trabajo es analizar las características del
mercado de las aplicaciones alojadas en Google Play Store para saber
cómo influyen las mismas en la popularidad de las aplicaciones (medido
por el número de instalaciones). De esta manera, se buscará investigar
el mercado de las App para decidir qué variables habría que tener en
cuenta para hacer de esta app popular. ¿Debería ser un juego o un
aplicativo informativo? ¿Bajo qué rotulo sería conveniente
clasificarla?.

En este marco, el trabajo se estructura de la siguiente manera: En
primer lugar, se realiza el análisis exploratorio y la limpieza de los
datos. En segundo lugar, se exploran cuáles son las características que
contribuyen a la popularidad de las aplicaciones. Por último, se tratará
de predecir la popularidad de las apps (medido por las instalaciones)

# Análisis exploratorio y transformación de las variables

Comenzamos por levantar la base de datos y explorar sus variables[^2]:

[^2]: <https://www.kaggle.com/code/akwamfoneventus/google-play-store-app-prep-cleaning-r>

    <https://www.kaggle.com/code/arstby/app-store-games-eda/report>

```{r}
#Cargamos la base y limpiamos los nombres del dataset 
apps <-  read_csv("Data/googleplaystore.csv") 


bd_apps <- apps %>% 
  clean_names()

#visualizamos los primeros valores
head(bd_apps) %>% 
  gt()


```

Composición de las variables:

```{r}
#visualizamos las variables 
bd_apps %>% 
  skimr::skim()

# variables por tipo 
bd_apps %>% vis_dat(warn_large_data = F)

#valores perdidos
vis_miss(bd_apps)
#solo hay en rating
```

Se observa que de 13 columnas, 12 contienen variables de tipo
"character" y 2 númericas. A continuación vamos a reconvertir algunas
variables.

`Rating` es la única variable que posee missings en su composición, esto
se debe a que en otras variables como `size` o `android version` se
encuentra el valor "*varies with device*" que será reemplazado por NA.
Además existen valores repetidos. Por lo que nos quedamos sólo con los
valores únicos

```{r}
nrow(bd_apps %>%
  distinct())



bd_apps <- bd_apps %>% 
  distinct()
```

```{r}
bd_apps %>% 
  filter(installs == "Free") %>% 
  gt()

```

Eliminamos esta observación dado que tiene un `rating` que supera los 5
puntos y una categoría que no coincide con la del resto de las apps.

Las variable instalaciones, precio y tamaño poseen caracteres. Vamos a
transformarlas para su posterior utilización. Respecto de `size` la
variable contiene "M" (MB) o "K" (KB). Asimismo se observa que existe el
valor *"varies with device"* . Esto es debido a que Google Play permite
publicar diferentes APK para cada aplicación. Cada uno dirigido a una
configuración de dispositivo diferente. Por lo que, al seleccionar
"instalar" el sistema Android selecciona los recursos apropiados para el
dispositivo. Para poder convertir esta variable a numérica se pasará
todo a KB. Es decir multiplicando los MB \* 1000, dado que 1 MB = 1000
KB. Sucede lo mismo con `Android versión` que posee valores
correspondientes a *"varies with device"*

```{r}

#pasamos a formato fecha la variable last_updated
bd_apps <- bd_apps %>%
  filter(app != "Life Made WI-Fi Touchscreen Photo Frame") %>% 
  mutate(last_updated = mdy(last_updated),
         installs = gsub("\\+",'',installs), #eliminamos los simbolos 
         installs = gsub(",",'',installs),
         installs = as.numeric(installs),
         reviews = as.numeric(reviews), #pasamos a numérico
         price = as.numeric(gsub("\\$", "", as.character(price))), #eliminamos los simbolos
         android_ver = gsub("Varies with device", NA, android_ver), #varies with device lo pasamos a NA
    android_ver = as.numeric(substr(android_ver, start = 1, stop = 3)),
     size_num = ifelse(grepl("M", size), as.numeric(sub("([0-9\\.]+)M", "\\1", size))*1000, as.numeric(sub("([0-9\\.]+)k", "\\1", size)))) %>% #dejamos un solo decimal 
  filter(type %in% c("Free", "Paid"))
    # Hay dos apps que tienen 0 o NA, vamos a eliminarlas y quedarnos solo con las que tienen Free o PAID en Type
  
bd_apps %>% 
  skimr::skim()
```

#### Type

```{r}

#transformamos type a binaria
bd_apps$type_bin <- ifelse(bd_apps$type == "Paid", 1, 0)

#mostramos el resultado
g2 <- bd_apps %>% 
  group_by(type) %>% 
  summarise(N=n()) %>% 
  ggplot(aes(N, reorder(type,N))) +
  geom_col(fill = "#009999") +
  theme_classic() +
  labs(x = " ",
       y = " ",
       title = "Distribución de aplicaciones por tipo (pago/gratuito") 


ggplotly(g2)

```

La variable `type` muestra si la aplicación es paga o gratuita, para
poder utilizarla en los análisis la transformaremos en una variable
binaria asignandole 1 si es paga y 0 si es gratuita

#### Content raiting

Vamos a modificar esta variable para generar rangos de edad

```{r}
bd_apps <- bd_apps %>%
  mutate(grupo_edades =  case_when(content_rating == "Everyone" ~ "4+",
                                     content_rating == "Everyone 10+" ~ "9+",
                                     content_rating == "Teen" ~ "12+",
                                     content_rating == "Mature 17+" ~ "17+",
                                     content_rating == "Unrated" ~ "9+",
                                   content_rating == "Adults only 18+" ~ "17+"))

bd_apps %>% 
  filter(content_rating == "Unrated") %>% 
  gt()

g1 <- bd_apps %>% 
  group_by(grupo_edades) %>% 
  summarise(N=n()) %>% 
  ggplot(aes(N, reorder(grupo_edades,N))) +
  geom_col(fill = "#009999") +
  theme_classic() +
  labs(x = "Número de aplicaciones",
       y = "Grupo de edades",
       title = "Distribución de aplicaciones por grupo de edades") 


ggplotly(g1)

```

Hay dos apps sin calificar que son Best CG Photography y DC Universe
Online Map. como son herramientas, vamos a clasificarlas como "Everyone"
osea +9. Hay solo 3 aplicaciones que corresponden a +18, se las
incorporará a +17.

```{r}

#vemos la distribución de los grupos de edad en las apps
edades <- bd_apps %>%
    group_by(grupo_edades) %>%
    summarize(Total = n()) %>%
    mutate(perc = round(Total/sum(Total) * 100)) %>%
    arrange(-perc)

perc_counts <- edades$perc
names(perc_counts) <- edades$grupo_edades

# Graficamos

waffle(perc_counts) + 
  theme_minimal() +
  theme(axis.text.y = element_blank(),
        axis.ticks.y = element_blank(),
        axis.text.x = element_blank(),
        plot.title = element_text(hjust = 0.5)) +
  labs(title = "Porcentaje de apps por grupos de edad")



```

```{r eval = FALSE }
rm(edades)
rm(perc_counts)
```

La mayoría de las aplicaciones está catalogada como "Everyone" o apta
para mayores de 4 años.

#### genres

```{r}
bd_apps %>%
  group_by(genres) %>%
  summarise(n = n()) %>% 
  head(15) %>% 
  gt()

#exploramos las etiquetas, dividimos las etiquetas 

generos <- bd_apps %>%
  separate_rows(genres, sep = ";") %>% 
 # separate_rows(genres, sep = "&") %>% 
  count(genres) %>% 
  arrange(desc(n))

g3 <- ggplot(generos, aes(x = genres, y = n)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  xlab("Género") +
  ylab("Frecuencia") +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(x = "Géneros",
       y = "N° de apps",
       title = "Distribución de aplicaciones por género") 


ggplotly(g3)

```

La variable `genres` contiene etiquetas que definen el género de la
aplicación. Es decir una app puede tener más de una etiqueta. Debido a
la cantidad de categorías que posee la variable se decide eliminarla
para el desarrollo de los posteriores modelos

### Valores Nulos

```{r}
# Valores nulos

md.pattern(bd_apps, rotate.names = TRUE, plot = TRUE)

# Visualización de perdidos
gg_miss_var(bd_apps, show_pct = T)

#Analizamos el patrón de los valores nulos
gg_miss_upset(bd_apps,nsets = 10)
```

Se observa que hay un patrón en los datos faltantes de `android_ver` ,
`rating` y `size_num` por lo que no es posible eliminar los valores
nulos.

#### Rating

Más arriba se observó que la variable `rating` tiene valores nulos.
Observamos la distribución de estos valores en relación a la cantidad de
descargas

```{r}

t2 <- bd_apps %>% 
  filter(is.na(rating)) %>% 
  count(reviews) %>% 
  mutate(porcentaje = round(n/1474*100, 2),
         porcentaje_acumulado = cumsum(porcentaje)) 


#analizamos los ratings por cantidad de reviews

t1 <- bd_apps %>% 
  filter(is.na(rating)) %>% 
  count(installs) %>% 
  mutate(porcentaje = round(n/1474*100, 2),
         porcentaje_acumulado = cumsum(porcentaje)) 

kable(list(t1, t2))



```

El 80% de las aplicaciones que poseen missings en la variable `rating`
tienen menos de 500 descargas y menos de 10 reviews. Esto se puede deber
a que como fueron poco descargadas todavía la gente no las ha puntuado o
algún error en el webscrapping.

```{r eval=FALSE, echo=FALSE}
rm(t1)
rm(t2)
```

#### Tamaño (size)

```{r}
bd_apps %>% 
  group_by(size_num) %>% 
  summarise(N= n()) %>% 
  arrange(desc(N)) %>% 
  head() %>% 
  gt()

```

De 10356 registros 1525 (15%) no poseen un tamaño definido por lo
expresado más arriba. Vamos a ver la distribución de esta variable:

```{r}
# histograma de la variable "size"
p1<- ggplot(bd_apps, aes(x = size_num)) + 
  geom_histogram(color="black", fill="lightblue", binwidth = 5000) +
  labs(title = "Distribución del tamaño de las aplicaciones",
       x = "Tamaño (KB)", y = "Frecuencia") +
  theme_minimal() +
  theme(plot.title = element_text(size=14, face="bold"),
        axis.title.x = element_text(size=12),
        axis.title.y = element_text(size=12),
        axis.text = element_text(size=10))

# densidad de la variable "size"
p2 <-ggplot(bd_apps, aes(x = size_num)) + 
  geom_density(color="black", fill="lightblue") +
  labs(x = "Tamaño (KB)", y = "Densidad") +
  theme_minimal() +
  theme(plot.title = element_text(size=14, face="bold"),
        axis.title.x = element_text(size=12),
        axis.title.y = element_text(size=12),
        axis.text = element_text(size=10))

grid.arrange(p1, p2, ncol=2) 


```

```{r eval=FALSE, echo=FALSE}
rm(p1)
rm(p2)
```

#### Android version

Hay 1352 filas que contienen NA porque corresponde a la categoría
"*varies with devices".*

```{r}
bd_apps %>%
  group_by(android_ver) %>%
  summarise(n = n()) %>%
  ggplot(aes(x = as.factor(android_ver), y = n, fill = android_ver)) +
  geom_bar(stat = "identity") +
  labs(x = "Versión de Android", y = "Frecuencia", fill = "Versión de Android") +
  theme_classic()
```

#### current_ver

```{r}
bd_apps %>%
  group_by(current_ver) %>%
  summarise(n = n()) %>% 
  arrange(desc(n)) %>% 
  head() %>% 
  gt()



```

La variable `current_ver` tiene 2833 valores únicos, el 25% de los
registros. Esto sugiere que no es muy informativa. Además, no puede ser
convertida a numérica ya que es una variable categorica que indica la
versión actual de la aplicación. **No siempre el número de versión es un
número continuo.** Por este motivo se decide prescindir de esta variable
para el posterior análisis

[A continuación utilizaremos la técnica de imputación múltiple del
paquete ´mice´ para los valores nulos]{.underline}

```{r,results='hide'}

#Imputamos los NA

imp <- mice(bd_apps[, c("size_num", "rating", "android_ver")])

```

```{r}

# Visualizamos la distribución de variables antes y después de la imputación
kableExtra::kable(summary(bd_apps[, c("size_num", "rating", "android_ver")]),caption = "Extructura variables previo a imputar")
kableExtra::kable(summary(complete(imp)[, c("size_num", "rating", "android_ver")]),caption = "Extructura variables imputadas")


# Agregamos las variables originales a la base imputada
bd_apps_imputed <- cbind(bd_apps[, setdiff(colnames(bd_apps), colnames(imp))], complete(imp))

# Renombrar las columnas imputadas
colnames(bd_apps_imputed)[17:19] <- paste0(colnames(bd_apps_imputed)[17:19], "_imp")

#sacamos las variables que no nos sirven o las ya imputadas y creamos la base que se va a utilizar para el desarrollo de la consigna
df_apps <- bd_apps_imputed %>% 
  select(-rating,
         -size,
         -size_num,
         -android_ver,
         -content_rating,
         -current_ver)

# Verificamos la estructura de la nueva base de datos
skimr::skim(df_apps)


```

```{r eval=FALSE, echo=FALSE}
#eliminamos los datasets 
rm(bd_apps)
rm(bd_apps_imputed)
rm(apps)

```

Volvemos a ver cómo quedó la estructura de los valores nulos

```{r}
# variables por tipo 
df_apps %>% vis_dat(warn_large_data = F)

#valores perdidos
vis_miss(df_apps)


```

```{r eval= FALSE, echo=FALSE}
rm(imp)
```

### Valores Atípicos

A continuación `boxplot.stats` calcula el límite inferior y superior de
cada variable, y luego suma los valores que se encuentran por debajo y
por encima del limite superior

```{r}
count_outliers <- function(x) {
  bp <- boxplot.stats(x)
  sum(x < bp$stats[1] | x > bp$stats[5])
}

bd_numerico <- df_apps %>% 
  select_if(is.numeric)



# Contamos los outliers en la base de datos de ejemplo
sapply(bd_numerico, count_outliers)


# Boxplots

plot1 <- ggplot(df_apps, aes(y = installs)) + 
  geom_boxplot(aes(fill = "installs")) +
  scale_fill_manual(values = '#FF689f', guide= FALSE) +
  ggtitle("Boxplot para la variable installs") +
  ylab("Cantidad") +
  theme_classic()

plot2 <- ggplot(df_apps, aes(y = price)) + 
  geom_boxplot(aes(fill = "price")) +
  scale_fill_manual(values = '#DC71FA', guide= FALSE) +
  ggtitle("Boxplot para la variable price") +
  ylab("Cantidad") +
  theme_classic()

plot3 <- ggplot(df_apps, aes(y = rating_imp )) + 
  geom_boxplot(aes(fill = "rating_imp")) +
  scale_fill_manual(values = '#00ABFD', guide= FALSE) +
  ylab("Cantidad") +
  theme_classic() + 
  ggtitle("Boxplot para la variable raiting")

# Boxplot de type_bin
plot4 <- ggplot(df_apps, aes(x = "", y = reviews)) +
  geom_boxplot(aes(fill = "reviews")) +
  scale_fill_manual(values = '#00C1AA', guide= FALSE)+
  ggtitle("Boxplot de type_bin")+
  ylab("Cantidad") +
  theme_classic()

plot5 <- ggplot(df_apps, aes(y = size_num_imp)) + 
  geom_boxplot(aes(fill = "size_num_imp")) +
  scale_fill_manual(values = '#39B600', guide= FALSE)+
  ggtitle("Boxplot para la variable size_num") +
  ylab("Tamaño en MB") +
  theme_classic()


plot6 <-ggplot(df_apps, aes(y = android_ver_imp  )) + 
  geom_boxplot(aes(fill = "android_ver_imp")) +
  scale_fill_manual(values = '#F37B59', guide= FALSE)+
  ggtitle("Boxplot para la variable android version") +
  ylab("Cantidad") +
  theme_classic()

grid.arrange(plot1, plot2, plot3, plot4, plot5, plot6, ncol = 2)



```

Se observa presencia de outliers en la mayoría de las variables
numéricas. Esto se debe a la dispersión de los datos y no a un error en
la medición. Es decir, hay aplicaciones con mayor precio o cantidad de
instalaciones que otras. El caso de `typebin` es porque es una variable
binaria por lo que no conviene imputar los outliers para no generar
cambios en su distribución.

En la variable `price` existen valores atípicos porque gran parte de la
muestra de apps es gratuita. En este caso se decide no imputar esos
valores, ya que son legítimos y representan el precio real de las
aplicaciones.

```{r eval=FALSE, echo=FALSE}
#Eliminamos para optimizar memoria
rm(plot1)
rm(plot2)
rm(plot3)
rm(plot4)
rm(plot5)
rm(plot6)
```

```{r}
quantile(df_apps$price, na.rm=TRUE)
```

El 75% de las apps son gratuitas. Para los análisis posteriores se
decidió omitir esta variable. Se utilizará solo `type`, es decir si la
aplicación es paga o gratuita

```{r}
df_apps <- df_apps %>% 
  select(-price)
```

`Reviews`

```{r}
ggplot(df_apps, aes(x = reviews)) +
  geom_histogram(bins = 30, color = "black", fill = "lightblue") + 
  labs(title = "Histograma de Reviews", x = "Número de Reviews", y = "Frecuencia")
  

summary(df_apps$reviews)
```

Se puede ver que la mayoría de las apps tienen pocas reviews. El 50%
tiene 1683 o menos. Por lo que se observa que hay algunos outliers.
También se puede observar que hay una gran variabilidad en la cantidad
de reseñas, con una media de 405944 y un valor máximo de 78158306, lo
que sugiere la presencia de outliers

Reemplazar los outliers de variables como `rating` y `android_ver` no la
consideramos apropiada debido a que, la primera solo tiene valores del 1
al 5; y, la segunda del 1 al 8.

```{r}
plot1 <- ggplot(df_apps, aes(x = rating_imp)) +
  geom_histogram(binwidth = 0.5, fill = "#00ABFD", color = "white") +
  ggtitle("Distribución de Rating") +
  xlab("Rating") +
  ylab("Frecuencia") +
  theme_classic()

plot_3 <- ggplot(df_apps, aes(x = rating_imp)) +
  geom_density(fill = "#00ABFD", color = "white") +
  ggtitle("Densidad de rating") +
  xlab("Rating") +
  ylab("Densidad") +
  theme_classic()


plot2 <- ggplot(df_apps, aes(x = android_ver_imp)) +
  geom_histogram(binwidth = 0.5, fill = "#00ABFD", color = "white") +
  ggtitle("Distribución de android_ver") +
  xlab("version android") +
  ylab("Frecuencia") +
  theme_classic()

plot4 <- ggplot(df_apps, aes(x = android_ver_imp)) +
  geom_density(fill = "#00ABFD", color = "white") +
  ggtitle("Densidad de android_ver") +
  xlab("versión android") +
  ylab("Densidad") +
  theme_classic()

grid.arrange(plot1, plot_3, plot2,plot4, ncol =2 )


```

A continuación se imputarán los valores atípicos para las variables
`installs`, `reviews` y `size` a través de `winzonrize` del paquete
`robustHD` para reducir el impacto de los valores extremos o atípicos.
Esta técnica se utiliza para reemplazar los outliers por los valores mas
cercanos.

```{r eval=FALSE, echo=FALSE }
rm(plot1)
rm(plot_3)
rm(plot2)
rm(plot4)
```

```{r}

#imputamos los outliers

df_final <- df_apps %>%
  mutate(installs = winsorize(installs, probs = c(0.05, 0.95)),
         reviews = winsorize(reviews, probs = c(0.05, 0.95)),
         size_num_imp = winsorize(size_num_imp, probs = c(0.05, 0.95)))



```

```{r eval=FALSE, echo=FALSE}
#eliminamos df_apps
rm(df_apps)

```

Analizamos la nueva distribución:

```{r}
bd_numerico2 <- df_final %>% 
  select_if(is.numeric)

# Contar los outliers en la base de datos de ejemplo
sapply(bd_numerico2, count_outliers)

# Crear el boxplot
plot1 <- ggplot(df_final, aes(y = installs)) + 
  geom_boxplot(aes(fill = "installs")) +
  scale_fill_manual(values = '#FF689f', guide= FALSE) +
  ggtitle("Boxplot para la variable installs") +
  ylab("Cantidad") +
  theme_classic()


plot5 <- ggplot(df_final, aes(y = size_num_imp)) + 
  geom_boxplot(aes(fill = "size_num_imp")) +
  scale_fill_manual(values = '#39B600', guide= FALSE)+
  ggtitle("Boxplot para la variable size_num") +
  ylab("Tamaño en MB") +
  theme_classic()

plot6 <-ggplot(df_final, aes(y = reviews  )) + 
  geom_boxplot(aes(fill = "reviews")) +
  scale_fill_manual(values = '#F37B59', guide= FALSE)+
  ggtitle("Boxplot para la variable android version") +
  ylab("Cantidad") +
  theme_classic()

grid.arrange(plot1,plot5, plot6, ncol = 1)


```

```{r eval=FALSE, echo=FALSE}
rm(plot1)
rm(plot5)
rm(plot6)
rm(bd_numerico)
rm(bd_numerico2)
```

### Popularidad \~ Instalaciones

#### Categorías

```{r}

g <- df_final %>% 
  group_by(category) %>% 
  summarise(N = n()) %>% 
  ggplot(aes(x = category, y = N, size = N, color = category)) +
  geom_point() +
  theme_classic()+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  labs(x = "", y = " ", title = "Cantidad de apps por categoría") +
  theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold")) +
  theme(legend.position = "none") 



ggplotly(g)
rm(g)
```

Se puede observar que de las categorías existentes la mayoría de las
apps se encuentran clasificadas como Family, Game y Tools. A
continuación se analizan cuales son las categorías más instaladas:

```{r}
g <- df_final %>% 
  group_by(category) %>% 
  summarise(descargas = sum(installs)) %>% 
  ggplot(aes(x = reorder(category,-descargas), y = descargas, size = descargas, color = category)) +
  geom_point() +
  theme_classic()+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  labs(x = "", y = " ", title = "Categorías más populares (Cantidad de instalaciones)", caption = "En millones de descargas") +
  theme(plot.title = element_text(hjust = 0.5, size = 14, face = "bold")) +
  theme(legend.position = "none") +
  scale_y_continuous(labels = scales::comma)

# bd_apps %>% 
#   group_by(category) %>% 
#   summarise(descargas = sum(installs)) %>% 
#   arrange(desc(descargas))

ggplotly(g)
rm(g)
```

Se puede observar que las categorías más populares son GAME y FAMILY

#### Tipo de app (gratuita o paga)

```{r}
g4 <- ggplot(df_final, aes(x=type, y=installs, fill=type)) +
  geom_boxplot() +
  scale_fill_brewer(palette = "Set2") +
  scale_y_continuous(labels = scales::comma) +
  theme_classic() +
  ggtitle(label = "Boxplot instalaciones por tipo") +
  guides(fill=FALSE)

ggplotly(g4)

rm(g4)
```

Las aplicaciones gratuitas son mas instaladas en general

#### Grupo de edades

```{r}
# Convertir a gráfico interactivo
p <- ggplot(df_final, aes(x = reorder(grupo_edades,installs), y = installs)) +
  geom_bar(stat = "identity", fill = "#FB8072") +
  labs(title = "Cantidad de instalaciones por grupos de edades",
       x = "Grupos de Edades", y = "Cantidad de instalaciones") +
  theme_classic() 

ggplotly(p)
rm(p)
```

Se puede observar que las apps más descargadas son las habilitadas para
+4 años (toda la familia)

#### Rating

```{r}

p <- df_final %>% 
  mutate(rating_imp = round(rating_imp,0)) %>% 
  ggplot(aes(x = reorder(rating_imp,installs), y = installs)) +
  geom_bar(stat = "identity", fill = "#FB8072") +
  labs(title = "Cantidad de instalaciones por rating",
       x = "Rating", y = "Cantidad de instalaciones") +
  theme_classic() 

ggplotly(p)
rm(p)
```

Las apps con mayor cantidad de instalaciones son las que tienen un
puntaje de 4 estrellas.

#### tamaño

```{r}
ggplot(df_final, aes(x = installs, y = size_num_imp, fill = size_num_imp)) +
  geom_boxplot(fill = "#FB8072") + theme_classic()  +
  scale_y_continuous(labels = scales::comma) +
  ylab("Instalaciones") +
  xlab("Tamaño") +
  ggtitle("Relación entre tamaño y cantidad de instalaciones") 


```

Las apps con mayor cantidad de instalaciones se encuentran entre 10000 y
30000 KB

#### Actualización

```{r}
plot1 <- df_final %>%
  group_by(last_updated) %>%
  summarise(total_installs = sum(installs)) %>%
  ggplot(aes(x = last_updated, y = total_installs)) +
  geom_line(color = "#FF689f", size = 1) +
  labs(x = "Fecha de actualización", y = "Instalaciones", 
       title = "Total de instalaciones por fecha de actualización") +
  theme_classic() +
  theme(plot.title = element_text(size = 14, face = "bold"),
        axis.text.x = element_text(angle = 90, vjust = 0.5, size = 10),
        axis.text.y = element_text(size = 10),
        axis.title = element_text(size = 12, face = "bold"),
        legend.title = element_blank(),
        legend.position = "none")

ggplotly(plot1)


```

Se puede observar que las aplicaciones más populares son las que poseen
actualización más reciente (2018). Por lo que, para incluirla en los
analisis convertimos la variable a año. Armamos una variable que sea
"Año de actualización" para poder incluirla en los análisis posteriores

```{r}
df_final <- df_final %>% 
  mutate(ano_act = year(last_updated))

#observamos la distribución por año
df_final %>% 
  group_by(ano_act) %>% 
  summarise(N=n()) %>% 
  gt()
```

# Análisis de la popularidad de las Apps de Google Play Store

### Árbol de decisión [^3]

[^3]: <https://www.kaggle.com/code/gabydel1982/telco-customer-churn-rboles-de-decisi-n>

El **árbol de decisión** es un modelo de aprendizaje automático que
divide los datos en subconjuntos más pequeños basados en diferentes
características y reglas. El objetivo es encontrar las variables que
tienen la mayor influencia en la popularidad (medido por la cantidad de
instalaciones) de una aplicación, para así encarar el desarrollo de la
aplicación que contribuya a difundir el *derecho de acceso* de la mejor
manera. De esta manera, se buscará identificar las variables más
importantes para explicar la variabilidad de la variable objetivo.

**Analizamos la correlación entre las variables numéricas:**

```{r}

#Guardamos el CSV
write.csv(df_final, "df_final.csv")

#armamos una matriz de correlación 
matriz_df <- df_final %>% 
  select_if(is.numeric)

matriz_df <- cor(matriz_df)
matriz_df

c1 <- matriz_df %>% 
  ggcorrplot:::ggcorrplot(type = "lower",  lab=TRUE, hc.order = TRUE, title = "Matriz de correlación R", colors = c("#6D9EC1", "white", "purple")) +
  theme(text = element_text(size = 10),
        axis.text.x =  element_text(angle=90, hjust=1, size = 7),
        axis.text.y =  element_text(size = 7))

ggplotly(c1)


#Borramos los datasets para optimizar memoria
rm(c1)
rm(matriz_df)

```

La variable con más correlación positiva es `reviews`

#### Preparación y estandarización de las variables

Creamos una variable llamada `popular` con la variable `installs` para
luego comparar con qué variable el modelo predice mejor.

```{r eval = FALSE}
#Borramos los datasets para optimizar memoria
rm(plot1)
rm(count_outliers)
rm(fa_apps)
```

```{r}
#convertimos a factor las variables categóricas



### Distribución de la variable installs
df_final %>% 
  group_by(installs) %>% 
  summarise(N=n()) %>% 
  gt() %>% 
  tab_header(title = "Apps por cantidad de instalaciones")

#Creo variables dummys y estandarizo las variables
df_accesin <- df_final %>% 
  mutate(category = as.factor(category),
         grupo_edades = as.factor(grupo_edades),
         ano_act = as.factor(ano_act),
         popular = ifelse(installs >= 100000, 1,0)) %>%
  select(-last_updated, -type, -genres)%>%  
  recipes::step_scale(all_numeric(), except = c("type_bin","popular", "installs")) %>% 
  select(-steps)


#df_accesin %>% group_by(android_ver_imp) %>% summarise(N=n())
#ponemos el nombre de la app como nombre de la fila 
df_accesin$app <- paste0(seq_len(nrow(df_accesin)), "_", df_accesin$app)
rownames(df_accesin) <- df_accesin$app


df_accesin_cat <- df_accesin %>% 
  select_if(is.factor) 

#Creating Dummy Variables
dummy<- data.frame(sapply(df_accesin_cat,function(x) data.frame(model.matrix(~x-1,data =df_accesin_cat))[,-1]))

dummy %>% 
  head(10) %>% 
  gt()

df_accesin_int <- df_accesin %>% 
  select_if(is.numeric) 

df_analisis <- cbind(df_accesin_int,dummy)

##Creamos un dataset con la variable popular y otro con la variable installs
df_popular <- df_analisis %>% 
  select(-installs)

accesin_final <- df_analisis %>% 
  select(-popular)

```

```{r eval=FALSE, echo=FALSE}
#Borramos los datasets para optimizar memoria
rm(df_accesin_int)
rm(df_accesin_cat)
rm(dummy)

```

Observamos la matriz de correlación con las variables binarias

```{r}
matriz_df <- accesin_final %>% 
  select_if(is.numeric)

matriz_df <- cor(matriz_df)

c1 <- matriz_df %>% 
  ggcorrplot:::ggcorrplot(type = "full",  lab=FALSE, hc.order = FALSE, colors = c("#6D9EC1", "white", "purple"), ggtheme = ggplot2::theme_classic) +
  ggtitle("Matriz de correlación R") +
  theme(text = element_text(size = 5),
        axis.text.x =  element_text(angle=90, hjust=1, size = 5),
        axis.text.y =  element_text(size = 5))

ggplotly(c1)

```

Las variables con mayor correlación son

```{r}
# Seleccionar las columnas que tienen una correlación mayor a 0.5
  
cols_sel <- matriz_df %>%
  abs() %>%
  as.data.frame() %>%
  rownames_to_column(var = "var1") %>%
  pivot_longer(cols = -var1, names_to = "var2", values_to = "cor") %>%
  filter(var1 != var2 & cor > 0.3) %>% 
  arrange(desc(cor))

cols_sel %>% 
  gt() %>% 
  tab_header(title = "Variables con mayor correlación")
```

#### Creamos el dataset de train y test

```{r}

#Creamos el dataset de train y test 

#fijamos una semilla
set.seed(583)
n <- nrow(accesin_final)
train_idx <- sample(1:n, n*0.7, replace = FALSE) # 70% para entrenamiento
train <- accesin_final[train_idx, ]
test <- accesin_final[-train_idx, ]

n_train = nrow(train)

#visualizamos la distribución
train %>% 
  group_by(installs) %>% 
  summarise(Prop = round(n()/n_train,3)) %>% 
  gt() %>%
  tab_options(page.width = "100") %>%
  tab_header(title = "Proporción de Instalaciones")


```

#### Modelo 1

```{r}

#creamos el modelo
model <- rpart(installs ~., data = train, method = 'class')

#Graficamos
rpart.plot(model, main = "Árbol de clasificación", extra = 101, under = TRUE, branch.lty = 1, shadow.col = "gray") 

#resumen del modelo creado
summary(model)
```

El resultado del primer modelo muestra que las variables con mayor
importancia son (en el siguiente orden): `reviews`, `size_num_imp`,
`ano_act.x2018`, `category.xGAME`, `grupo_edades.x4.`, `rating_imp`,
`type`

```{r}
# Aplicamos el modelo a los datos de prueba
predict_test <- predict(model, test, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test$installs, predict_test)
table_mat

# Calculamos la precisión del modelo
accuracy_train <- function(fit) {
    predict_unseen_train <- predict(fit, train, type = 'class')
    table_mat <- table(train$installs, predict_unseen_train)
    accuracy_train <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_train
}


accuracy_test <- function(fit) {
    predict_unseen <- predict(fit, test, type = 'class')
    table_mat <- table(test$installs, predict_unseen)
    accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_Test
}


print(paste('Accuracy para train', accuracy_train(model)))
print(paste('Accuracy para test', accuracy_test(model)))
```

El valor de 0.67 para la exactitud (accuracy) del modelo puede
considerarse relativamente bueno.

```{r}
# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model, newdata = test, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test$installs))

# Tabla de contingencia
table_test <- table(test$installs, pred_test)

# Precisión por instalaciones
precision <- diag(table_test) / colSums(table_test)

# Recall por instalaciones
recall <- diag(table_test) / rowSums(table_test)

# Graficar precision y recall en un gráfico de barras
barplot(precision, ylim = c(0, 1), main = "Precisión por instalaciones", xlab = "cantidad", ylab = "Precisión")
barplot(recall, ylim = c(0, 1), main = "Recall por instalaciones", xlab = "cantidad", ylab = "Recall")


```

El modelo clasifica correctamente el 67,36% de las muestras. En cuanto a
la matriz de confusión, muestra que el modelo tiene dificultades para
clasificar correctamente las clases de muestra más bajas (0, 1 y 5) y
las clases de muestra más altas (5000, 50000 y 100000).

#### Modelo 2

Vamos a ajustar este modelo en base a `tune` que prueba diferentes
valores de hiperparámetros y devuelve el conjunto de valores que produce
el mejor modelo. En este caso se utilizará `cp` para controlar la
complejidad del modelo:

```{r}

# Define the range of values for the cp parameter
cp_values <- seq(0.001, 0.1, by = 0.001)

# Create the tuning grid
tune_grid <- data.frame(cp = cp_values)

# Fit the model with cross-validation and the tuning grid
fit <- train(
  installs ~ .,
  data = train,
  method = "rpart",
  tuneGrid = tune_grid,
  trControl = trainControl(method = "cv", number = 10, verboseIter = TRUE)
)

model_2 <- rpart(installs ~ ., data = train, method = "class", control = rpart.control(cp = fit$bestTune$cp))

# Plot the decision tree
rpart.plot(model_2, extra = 1,main = "Arbol" )

summary(model_2)


# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_2, newdata = test, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test$installs))

predict_test <- predict(model_2, test, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test$installs, predict_test)
table_mat

print(paste('Accuracy para train', accuracy_train(model_2)))
print(paste('Accuracy para test', accuracy_test(model_2)))

```

En comparación con el modelo 2, podemos ver que el modelo 1 tiene una
accuracy menor (67,36% vs 69%), un kappa menor (0,5626 vs 0.5939) y una
sensibilidad mucho menor para las clases 0, 1, 5 y 50 y una sensibilidad
mayor para las clases 1000, 50000 y 100000.

El accuracy tanto para `train` como para `test` son similares, lo cual
es una buena señal de que no hay overfitting o sobreajuste

```{r}
# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_2, newdata = test, type = "class")

# Tabla de contingencia
table_test <- table(test$installs, pred_test)

# Precisión por instalaciones
precision <- diag(table_test) / colSums(table_test)

# Recall por instalaciones
recall <- diag(table_test) / rowSums(table_test)



# Graficar precision y recall en un gráfico de barras
barplot(precision, ylim = c(0, 1), main = "Precisión por instalaciones", xlab = "cantidad", ylab = "Precisión")
barplot(recall, ylim = c(0, 1), main = "Recall por instalaciones", xlab = "cantidad", ylab = "Recall")

```

#### Arbol de decisión con la variable popular

Mas arriba se creó una variable `popular` (binaria) en base a `installs`
a partir de la distribución de la cantidad de instalaciones, aquellas
apps con **\> 100000** instalaciones se las consideró **populares**. Se
tratará de predecir la popularidad de las apps en base a esta variable y
comparar si el modelo predice mejor que con `installs`

```{r}
#fijamos una semilla
set.seed(583)
n <- nrow(df_popular)
train_idx <- sample(1:n, n*0.7, replace = FALSE) # 70% para entrenamiento
train_pop <- df_popular[train_idx, ]
test_pop <- df_popular[-train_idx, ]

n_train = nrow(train_pop)
train_pop %>% 
  group_by(popular) %>% 
  summarise(Prop = round(n()/n_train,3)) %>% 
  gt() %>%
  tab_options(page.width = "100") %>%
  tab_header(title = "Proporción de Instalaciones")

```

Realizamos el modelo:

```{r}
#creamos el modelo
model_pop <- rpart(popular ~., data = train_pop, method = 'class')

#Graficamos el arbol
# fancyRpartPlot(model, type = 1, palettes=c("Greys", "Blues"), main = "Arbol de Clasificación - Modelo 1", caption = "Por la cantidad de instalaciones")

rpart.plot(model_pop, main = "Árbol de clasificación", extra = 101, under = TRUE, branch.lty = 1, shadow.col = "gray") 

#resumen del modelo creado
summary(model_pop)

predict_test <- predict(model_pop, test_pop, type = "class") 

# Creamos una tabla de contingencia para evaluar la precisión
table_mat <- table(test_pop$popular, predict_test)
table_mat


accuracy_train <- function(fit) {
    predict_unseen_train <- predict(fit, train_pop, type = 'class')
    table_mat <- table(train_pop$popular, predict_unseen_train)
    accuracy_train <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_train
}


accuracy_test <- function(fit) {
    predict_unseen <- predict(fit, test_pop, type = 'class')
    table_mat <- table(test_pop$popular, predict_unseen)
    accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_Test
}

print(paste('Accuracy para train', accuracy_train(model_pop)))
print(paste('Accuracy para test', accuracy_test(model_pop)))


# Obtener las predicciones del modelo en el conjunto de prueba
pred_test <- predict(model_pop, newdata = test_pop, type = "class")

# Matriz de confusión
confusionMatrix(table(pred_test, test_pop$popular))


predictions <- predict(model_pop, newdata = test, type = "prob")[, 2]


roc_curve <- roc(test_pop$popular ~ predictions)
plot(roc_curve) 
auc(roc_curve)
```

Al utilizar la variable dependiente `popular` en lugar de `installs`, el
modelo no toma en cuenta todas las variabilidades de `installs`. Sin
embargo, `model_pop` es más preciso para la predicción de la popularidad

Respecto a la **curva ROC**, el AUC es de 0.9405 lo que indica que el
modelo tiene una buena capacidad para clasificar

La matriz de confusión muestra que el `model_pop` tiene una precisión
del 94.27%, con una sensibilidad del 92.18% y una especificidad del
95.92%. Además, Kappa indica una fuerte concordancia entre las
predicciones del modelo y los valores reales observados.

Las posibles variables predictoras son `reviews` y `ano_act.x2018` junto
con `size_num_imp`, `rating_imp` y `type_bin`. La precisión del modelo
es delel 94%, y la probabilidad de clasificación correcta para la 1
(popular) es de 92.18% y para 0 es de 95.92%. La gratuidad de las apps,
un rating mayor y las apps con mayor tamaños son las que tienen más
relación con la popularidad de las apps:

```{r}

p1 <- ggplot(data = train_pop, aes(x = type_bin, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Type", y = "Popularidad") + 
  ggtitle("Popularidad x type")+
  theme_classic()  +
  theme(plot.title = element_text(size = 10))

p2 <- ggplot(data = train_pop, aes(x = rating_imp, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "rating", y = "") + 
  ggtitle("Popularidad x rating") + 
    theme_classic() + 
    theme(plot.title = element_text(size = 10))

p3 <- ggplot(data = train_pop, aes(x = size_num_imp, y = popular)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "tamaño", y = "") + 
  ggtitle("Popularidad x tamaño") +
  theme_classic()  +
  theme(plot.title = element_text(size = 10))



cowplot::plot_grid(p1, p2, p3, ncol = 3, align = "h") 



```

```{r eval = FALSE}
# Limpiamos memoria 
rm(fit, model,model_2,model_pop,p1,p2,p3, predict_test, predictions, roc1, roc2, roc_test,roc_curve, test_pop, test, train, train_pop, tune_grid, accuracy, cp_values, n, n_train, precision, pred_test, recall,table_mat, table_test, train_idx, df_analisis, accuracy_test,accuracy_Test,accuracy_train,df_final)
```

## ¿Se puede predecir la popularidad de una APP?

### Regresión Logística[^4]

[^4]: <https://www.kaggle.com/code/gabydel1982/telco-customer-churn-logisticregression-untref>

En función del objetivo del trabajo *"desarrollar una app de
promoción"*, se buscará elaborar un modelo que permita predecir la
probabilidad de que una aplicación sea popular en función de sus
características, para contribuir en las decisiones sobre el desarrollo y
estrategia de marketing de la App.

Vamos a utilizar `df_popular`

```{r}

# Regresión logística
library(caTools) #muestra
library(MASS) #stepAIC

df_popular %>% 
  head(5) %>% 
  gt()

#Dividimos la base en train y validation
set.seed(1120)
indices = sample.split(df_popular$popular, SplitRatio = 0.7)
train = df_popular[indices,]
validation = df_popular[!(indices),]
```

#### Modelo 1

```{r}
# Primer modelo con todas las variables
model_1 = glm(popular ~ ., data = train, family = "binomial")
summary(model_1) 
```

Las variables con mayor significancia son "reviews", "type_bin",
"rating_imp" y "category.xFINANCE". A continuación se muestra en una
tabla las variables con significancia estadística del modelo 1:

| **Variable**                  | **P-valor**           |
|-------------------------------|-----------------------|
| reviews                       | \< 0.0000000000000002 |
| type_bin                      | \< 0.0000000000000002 |
| rating_imp                    | 0.000000000256        |
| category.xBOOKS_AND_REFERENCE | 0.000120              |
| category.xBUSINESS            | 0.000003146100        |
| category.xCOMICS              | 0.003096              |
| category.xCOMMUNICATION       | 0.001129              |
| category.xDATING              | 0.006090              |
| category.xEVENTS              | 0.029426              |
| category.xFAMILY              | 0.000304              |
| category.xFINANCE             | 0.000000543376        |
| category.xGAME                | 0.000801              |
| category.xHEALTH_AND_FITNESS  | 0.002626              |
| category.xLIBRARIES_AND_DEMO  | 0.045199              |
| category.xLIFESTYLE           | 0.000064984971        |
| category.xMAPS_AND_NAVIGATION | 0.002266              |
| category.xMEDICAL             | 0.000008479370        |
| category.xNEWS_AND_MAGAZINES  | 0.000208              |
| category.xPERSONALIZATION     | 0.002230              |
| category.xPRODUCTIVITY        | 0.001483              |
| category.xSHOPPING            | 0.028897              |
| category.xSOCIAL              | 0.000031306821        |
| category.xSPORTS              | 0.000006654342        |
| category.xTOOLS               | 0.001749              |
| category.xTRAVEL_AND_LOCAL    | 0.004953              |
| category.xVIDEO_PLAYERS       | 0.007778              |
| grupo_edades.x17.             | 0.065640              |
| grupo_edades.x4.              | 0.019739              |

#### Modelo 2

Se utilizará `stepAIC` para la selección de variables, se trata de un
proceso iterativo que busca agregar o eliminar variables con el fin de
obtener un subconjunto de variables que proporcione el modelo más
óptimo. El modelo seleccionado es el que tiene el valor mínimo en el AIC

```{r}
#seleccionamos el método más optimo
model_2<- stepAIC(model_1, direction = "backward", steps = 100)
summary(model_2)
```

Las variables con el coeficiente el p-valor más alto son **`type_bin`**,
**`reviews`**, **`category.xBOOKS_AND_REFERENCE`**,
**`category.xBUSINESS`**, **`category.xCOMICS`**,
**`category.xFINANCE`**, **`category.xSPORTS`**,
**`category.xVIDEO_PLAYERS`** y **`category.xSOCIAL`**. Al mismo tiempo,
**`category.xSHOPPING`**, **`category.xEVENTS`**, **`grupo_edades.x17`**
y **`ano_act.x2014`** no son estadísticamente significativas por lo que
podrían eliminarse del análisis.

Se utilizará el **factor de inflación de la varianza (vif)** para
eliminar los predictores redundantes o las variables que tienen una alta
multicolinealidad entre ellos. El VIF mide la cantidad de varianza de
una variable que se puede explicar por otras variables en el modelo. Un
VIF de 1 indica que la variable no está correlacionada con otras
variables en el modelo, mientras que un VIF superior a 1 indica que la
variable está correlacionada con otras variables en el modelo.

```{r}
car::vif(model_2)
```

Se observa que la mayoría de las variables tienen un VIF entre 1 y 2, lo
que sugiere que no hay una multicolinealidad importante presente en el
modelo. De esta manera, *"un predictor que tiene un VIF de 2 o menos
generalmente se considera seguro y se puede suponer que no está
correlacionado con otras variables predictoras".*

#### Modelo 3

Se aplicará el modelo_2 sin las variables sin significancia estadística
del `modelo_2` (**`category.xSHOPPING`**, **`category.xEVENTS`**,
**`grupo_edades.x17`** y **`ano_act.x2014`**)

```{r}
model_3 <- glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
    category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION  + category.xFAMILY + 
    category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
    category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
    category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
    category.xPRODUCTIVITY  + category.xSOCIAL + 
    category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
    category.xVIDEO_PLAYERS  + ano_act.x2016 + ano_act.x2017 + category.xDATING + grupo_edades.x4., family = "binomial", data = train)
summary(model_3)
car::vif(model_3)
```

\

Respecto a los vectores de inflación todas las variables se encuentran
entre 1 y 2. Se observa que `category.xDATING` y `grupo_edades.x4.` no
tienen significancia estadística para un nivel de significancia del 5%
por lo que se realizará un `modelo_4` sin estas variables:

```{r}
model_4 <- glm(formula = popular ~ reviews + type_bin + rating_imp + category.xBOOKS_AND_REFERENCE + 
    category.xBUSINESS + category.xCOMICS + category.xCOMMUNICATION  + category.xFAMILY + 
    category.xFINANCE + category.xGAME + category.xHEALTH_AND_FITNESS + 
    category.xLIFESTYLE + category.xMAPS_AND_NAVIGATION + category.xMEDICAL + 
    category.xNEWS_AND_MAGAZINES + category.xPERSONALIZATION + 
    category.xPRODUCTIVITY  + category.xSOCIAL + 
    category.xSPORTS + category.xTOOLS + category.xTRAVEL_AND_LOCAL + 
    category.xVIDEO_PLAYERS  + ano_act.x2016 + ano_act.x2017, family = "binomial", data = train)

summary(model_4)
car::vif(model_4)
```

Todas las variables tienen significancia estadística en este último
modelo

```{r}
# Obtener los residuos
residuos <- residuals(model_4, type = "deviance")
summary(residuos) 

par(mfrow=c(1, 2))

plot(model_3, main="Modelo 3", pch=19, cex=1, which=1)
plot(model_4, main="Modelo 4", pch=19, cex=1, which=1)


```

Se puede observar que la media de los residuos es cercana a cero, lo que
indica que el modelo tiene un buen ajuste en términos generales. Al
mismo tiempo, hay valores extremos en los residuos, lo que puede indicar
la presencia de valores atípicos o errores en el modelo. Se elegirá el
`modelo_4` como modelo final.

Analizamos los **Odds Ratio**

```{r}
final_model <- model_4

#calculamos los ods ratio
exp(coef(final_model))
```

El Odd Ratio indica cuántas veces más probable es que ocurra un evento
dado (que la app sea popular), cuando se compara un cambio en una unidad
de la variable `popular`.

#### Evaluación del modelo

```{r}
pred <- predict(final_model, type = "response", newdata = validation)
summary(pred)
validation$prob <- pred

# Using probability cutoff of 50%.

pred_popular <- factor(ifelse(pred >= 0.50, "Yes", "No"))
actual_popular <- factor(ifelse(validation$popular==1,"Yes","No"))
table(actual_popular,pred_popular) 
```

Vamos a calcular la **sensibilidad**, la **especificidad** y
**accuracy** con un corte de 0.50

```{r}
cutoff_popular <- factor(ifelse(pred >=0.50, "Yes", "No"))
conf_final <- confusionMatrix(cutoff_popular, actual_popular, positive = "Yes")
accuracy <- conf_final$overall[1]
sensitivity <- conf_final$byClass[1]
specificity <- conf_final$byClass[2]
accuracy
sensitivity
specificity
```

La sensibilidad nos indica la capacidad de nuestro estimador para dar
como casos positivos. En este caso, nuestro modelo tiene una
sensibilidad de 0.92. La especificidad nos indica la capacidad de
nuestro estimador para dar como casos negativos, el `model_4` posee un
nivel de especificidad de 0.97, y, por último, Accuracy es lo que mide
en base a la diagonal cuantos de las apps populares reales (0.94).

```{r}
perform_app <- function(cutoff) 
{
  predicted_popular <- factor(ifelse(pred >= cutoff, "Yes", "No"))
  conf <- confusionMatrix(predicted_popular, actual_popular, positive = "Yes")
  accuray <- conf$overall[1]
  sensitivity <- conf$byClass[1]
  specificity <- conf$byClass[2]
  out <- t(as.matrix(c(sensitivity, specificity, accuray))) 
  colnames(out) <- c("sensitivity", "specificity", "accuracy")
  return(out)
}


options(repr.plot.width =8, repr.plot.height =6)
summary(pred)
s = seq(0.01,0.80,length=100)
OUT = matrix(0,100,3)

for(i in 1:100)
{
  OUT[i,] = perform_app(s[i])
} 

plot(s, OUT[,1],xlab="Cutoff",ylab="Value",cex.lab=1.5,cex.axis=1.5,ylim=c(0,1),
     type="l",lwd=2,axes=FALSE,col=2)
axis(1,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.5)
axis(2,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.5)
lines(s,OUT[,2],col="darkgreen",lwd=2)
lines(s,OUT[,3],col=4,lwd=2)
box()
legend("bottom",col=c(2,"darkgreen",4,"darkred"),text.font =3,inset = 0.02,
       box.lty=0,cex = 0.8, 
       lwd=c(2,2,2,2),c("Sensitivity","Specificity","Accuracy"))
abline(v = 0.32, col="red", lwd=1, lty=2)
axis(1, at = seq(0.1, 1, by = 0.1))

#cutoff <- s[which(abs(OUT[,1]-OUT[,2])<0.01)]
```

Según los resultados, el modelo es es capaz de predecir correctamente el
94.9% de los casos.


Trabajo Final - Estadística Aplicada a la Investigación de Mercado

Ariana Bard

1 Aplicaciones de Google Play Store

2 Análisis exploratorio y transformación de las variables

2.0.0.1 Type

2.0.0.2 Content raiting

2.0.0.3 genres

2.0.1 Valores Nulos

2.0.1.1 Rating

2.0.1.2 Tamaño (size)

2.0.1.3 Android version

2.0.1.4 current_ver

2.0.2 Valores Atípicos

2.0.3 Popularidad ~ Instalaciones

2.0.3.1 Categorías

2.0.3.2 Tipo de app (gratuita o paga)

2.0.3.3 Grupo de edades

2.0.3.4 Rating

2.0.3.5 tamaño

2.0.3.6 Actualización

3 Análisis de la popularidad de las Apps de Google Play Store

3.0.1 Árbol de decisión ³

3.0.1.1 Preparación y estandarización de las variables

3.0.1.2 Creamos el dataset de train y test

3.0.1.3 Modelo 1

3.0.1.4 Modelo 2

3.0.1.5 Arbol de decisión con la variable popular

3.1 ¿Se puede predecir la popularidad de una APP?

3.1.1 Regresión Logística⁴

3.1.1.1 Modelo 1

3.1.1.2 Modelo 2

3.1.1.3 Modelo 3

3.1.1.4 Evaluación del modelo

grupo_edades.x4.	ano_act.x2017	ano_act.x2018
1	0	1
1	0	1
1	0	1
0	0	1
1	0	1
1	1	0
1	0	1
1	0	1
1	1	0
1	0	1

grupo_edades.x4.	ano_act.x2017	ano_act.x2018
1	0	1
1	0	1
1	0	1
0	0	1
1	0	1
1	1	0
1	0	1
1	0	1
1	1	0
1	0	1

Trabajo Final - Estadística Aplicada a la Investigación de Mercado

Ariana Bard

1 Aplicaciones de Google Play Store

2 Análisis exploratorio y transformación de las variables

2.0.0.1 Type

2.0.0.2 Content raiting

2.0.0.3 genres

2.0.1 Valores Nulos

2.0.1.1 Rating

2.0.1.2 Tamaño (size)

2.0.1.3 Android version

2.0.1.4 current_ver

2.0.2 Valores Atípicos

2.0.3 Popularidad ~ Instalaciones

2.0.3.1 Categorías

2.0.3.2 Tipo de app (gratuita o paga)

2.0.3.3 Grupo de edades

2.0.3.4 Rating

2.0.3.5 tamaño

2.0.3.6 Actualización

3 Análisis de la popularidad de las Apps de Google Play Store

3.0.1 Árbol de decisión 3

3.0.1.1 Preparación y estandarización de las variables

3.0.1.2 Creamos el dataset de train y test

3.0.1.3 Modelo 1

3.0.1.4 Modelo 2

3.0.1.5 Arbol de decisión con la variable popular

3.1 ¿Se puede predecir la popularidad de una APP?

3.1.1 Regresión Logística4

3.1.1.1 Modelo 1

3.1.1.2 Modelo 2

3.1.1.3 Modelo 3

3.1.1.4 Evaluación del modelo

3.0.1 Árbol de decisión ³

3.1.1 Regresión Logística⁴

grupo_edades.x4.	ano_act.x2017	ano_act.x2018
1	0	1
1	0	1
1	0	1
0	0	1
1	0	1
1	1	0
1	0	1
1	0	1
1	1	0
1	0	1