Titanic

Árboles de decisión

Los árboles de decisión son modelos predictivos que utilizan una estructura jerárquica de decisiones en forma de árbol. Cada nodo interno del árbol representa una característica del conjunto de datos, cada borde representa una posible respuesta a esa característica, y cada hoja del árbol representa una predicción o clasificación.

Paso 1. Importar librerías

#install.packages("readxl")
library(readxl)

Paso 2. Cargar la base de datos

Titanic <- read_xls("Titanic.xls")

## Warning: Coercing text to numeric in M1306 / R1306C13: '328'

Paso 3. Entender la base de datos

summary(Titanic)

##      pclass         survived         name               sex           
##  Min.   :1.000   Min.   :0.000   Length:1309        Length:1309       
##  1st Qu.:2.000   1st Qu.:0.000   Class :character   Class :character  
##  Median :3.000   Median :0.000   Mode  :character   Mode  :character  
##  Mean   :2.295   Mean   :0.382                                        
##  3rd Qu.:3.000   3rd Qu.:1.000                                        
##  Max.   :3.000   Max.   :1.000                                        
##                                                                       
##       age              sibsp            parch          ticket         
##  Min.   : 0.1667   Min.   :0.0000   Min.   :0.000   Length:1309       
##  1st Qu.:21.0000   1st Qu.:0.0000   1st Qu.:0.000   Class :character  
##  Median :28.0000   Median :0.0000   Median :0.000   Mode  :character  
##  Mean   :29.8811   Mean   :0.4989   Mean   :0.385                     
##  3rd Qu.:39.0000   3rd Qu.:1.0000   3rd Qu.:0.000                     
##  Max.   :80.0000   Max.   :8.0000   Max.   :9.000                     
##  NA's   :263                                                          
##       fare            cabin             embarked             boat          
##  Min.   :  0.000   Length:1309        Length:1309        Length:1309       
##  1st Qu.:  7.896   Class :character   Class :character   Class :character  
##  Median : 14.454   Mode  :character   Mode  :character   Mode  :character  
##  Mean   : 33.295                                                           
##  3rd Qu.: 31.275                                                           
##  Max.   :512.329                                                           
##  NA's   :1                                                                 
##       body        home.dest        
##  Min.   :  1.0   Length:1309       
##  1st Qu.: 72.0   Class :character  
##  Median :155.0   Mode  :character  
##  Mean   :160.8                     
##  3rd Qu.:256.0                     
##  Max.   :328.0                     
##  NA's   :1188

str(Titanic)

## tibble [1,309 × 14] (S3: tbl_df/tbl/data.frame)
##  $ pclass   : num [1:1309] 1 1 1 1 1 1 1 1 1 1 ...
##  $ survived : num [1:1309] 1 1 0 0 0 1 1 0 1 0 ...
##  $ name     : chr [1:1309] "Allen, Miss. Elisabeth Walton" "Allison, Master. Hudson Trevor" "Allison, Miss. Helen Loraine" "Allison, Mr. Hudson Joshua Creighton" ...
##  $ sex      : chr [1:1309] "female" "male" "female" "male" ...
##  $ age      : num [1:1309] 29 0.917 2 30 25 ...
##  $ sibsp    : num [1:1309] 0 1 1 1 1 0 1 0 2 0 ...
##  $ parch    : num [1:1309] 0 2 2 2 2 0 0 0 0 0 ...
##  $ ticket   : chr [1:1309] "24160" "113781" "113781" "113781" ...
##  $ fare     : num [1:1309] 211 152 152 152 152 ...
##  $ cabin    : chr [1:1309] "B5" "C22 C26" "C22 C26" "C22 C26" ...
##  $ embarked : chr [1:1309] "S" "S" "S" "S" ...
##  $ boat     : chr [1:1309] "2" "11" NA NA ...
##  $ body     : num [1:1309] NA NA NA 135 NA NA NA NA NA 22 ...
##  $ home.dest: chr [1:1309] "St Louis, MO" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" ...

Paso 4. Filtrar base de datos

Titanic <- Titanic[,c("pclass","age","sex","survived")]
Titanic$survived <- as.factor(ifelse(Titanic$survived==0, "Murio", "Sobrevive"))
Titanic$pclass <- as.factor(Titanic$pclass)
Titanic$sex <-  as.factor(Titanic$sex)
str(Titanic)

## tibble [1,309 × 4] (S3: tbl_df/tbl/data.frame)
##  $ pclass  : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
##  $ age     : num [1:1309] 29 0.917 2 30 25 ...
##  $ sex     : Factor w/ 2 levels "female","male": 1 2 1 2 1 2 1 2 1 2 ...
##  $ survived: Factor w/ 2 levels "Murio","Sobrevive": 2 2 1 1 1 2 2 1 2 1 ...

sum(is.na(Titanic))

## [1] 263

sapply(Titanic, function(x) sum(is.na(x)))

##   pclass      age      sex survived 
##        0      263        0        0

Titanic <- na.omit(Titanic)

Paso 5. Crear árbol de decisión

# install.packages("rpart")
library(rpart)
arbol <- rpart(formula=survived ~ ., data = Titanic)
arbol

## n= 1046 
## 
## node), split, n, loss, yval, (yprob)
##       * denotes terminal node
## 
##  1) root 1046 427 Murio (0.59177820 0.40822180)  
##    2) sex=male 658 135 Murio (0.79483283 0.20516717)  
##      4) age>=9.5 615 110 Murio (0.82113821 0.17886179) *
##      5) age< 9.5 43  18 Sobrevive (0.41860465 0.58139535)  
##       10) pclass=3 29  11 Murio (0.62068966 0.37931034) *
##       11) pclass=1,2 14   0 Sobrevive (0.00000000 1.00000000) *
##    3) sex=female 388  96 Sobrevive (0.24742268 0.75257732)  
##      6) pclass=3 152  72 Murio (0.52631579 0.47368421)  
##       12) age>=1.5 145  66 Murio (0.54482759 0.45517241) *
##       13) age< 1.5 7   1 Sobrevive (0.14285714 0.85714286) *
##      7) pclass=1,2 236  16 Sobrevive (0.06779661 0.93220339) *

#install.packages("rpart.plot")
library(rpart.plot)
rpart.plot(arbol)

prp(arbol,extra = 7,prefix = "fraccion")

Paso 6. Conclusiones

1. Las más altas probabilidades de sobrevivir en el Titanic son niño varón menor de 9.5 años de 1° y 2° clase (100%), y mujeres en 1° y 2° clase (93%).
   
2. Las más bajas probabilidades de sobrevivir en el Titanic son los hombres mayores de 9.5 años (18%), y los hombres menores de 9.5 años en 3° clase (38%).