Árbol de decisión - Titanic

Teoría

El árbol de decisión es un diagrama de Aprendizaje Automático que modelas las opciones, eventos y posibles resultados de una decisión de forma visual.
Sus partes principales son:

• Nodo raíz: Inicio del diagrama.
  
• Ramas: Opciones disponible,
  
• Nodos internos:Nuevas decisiones.
  
• Hojas: Resultado final de cada camino.
  ## Importar la base de datos

#file.choose()
titanic <- read.csv("/Users/annaluisarochalopez/Desktop/titanic.csv")

Entender la base de datos

summary(titanic)

##      pclass         survived         name               sex           
##  Min.   :1.000   Min.   :0.000   Length:1310        Length:1310       
##  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                                        
##  NA's   :1       NA's   :1                                            
##       age              sibsp            parch          ticket         
##  Min.   : 0.1667   Min.   :0.0000   Min.   :0.000   Length:1310       
##  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   :264       NA's   :1        NA's   :1                         
##       fare            cabin             embarked             boat          
##  Min.   :  0.000   Length:1310        Length:1310        Length:1310       
##  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   :2                                                                 
##       body        home.dest        
##  Min.   :  1.0   Length:1310       
##  1st Qu.: 72.0   Class :character  
##  Median :155.0   Mode  :character  
##  Mean   :160.8                     
##  3rd Qu.:256.0                     
##  Max.   :328.0                     
##  NA's   :1189

str(titanic)

## 'data.frame':    1310 obs. of  14 variables:
##  $ pclass   : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ survived : int  1 1 0 0 0 1 1 0 1 0 ...
##  $ name     : chr  "Allen, Miss. Elisabeth Walton" "Allison, Master. Hudson Trevor" "Allison, Miss. Helen Loraine" "Allison, Mr. Hudson Joshua Creighton" ...
##  $ sex      : chr  "female" "male" "female" "male" ...
##  $ age      : num  29 0.917 2 30 25 ...
##  $ sibsp    : int  0 1 1 1 1 0 1 0 2 0 ...
##  $ parch    : int  0 2 2 2 2 0 0 0 0 0 ...
##  $ ticket   : chr  "24160" "113781" "113781" "113781" ...
##  $ fare     : num  211 152 152 152 152 ...
##  $ cabin    : chr  "B5" "C22 C26" "C22 C26" "C22 C26" ...
##  $ embarked : chr  "S" "S" "S" "S" ...
##  $ boat     : chr  "2" "11" "" "" ...
##  $ body     : int  NA NA NA 135 NA NA NA NA NA 22 ...
##  $ home.dest: chr  "St Louis, MO" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" ...

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)

## 'data.frame':    1310 obs. of  4 variables:
##  $ pclass  : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
##  $ age     : num  29 0.917 2 30 25 ...
##  $ sex     : Factor w/ 3 levels "","female","male": 2 3 2 3 2 3 2 3 2 3 ...
##  $ survived: Factor w/ 2 levels "Murio","Sobrevive": 2 2 1 1 1 2 2 1 2 1 ...

sum(is.na(Titanic))

## [1] 266

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

##   pclass      age      sex survived 
##        1      264        0        1

Titanic <- na.omit(Titanic)

Crear arbol de decisión

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

## Warning: package 'rpart' was built under R version 4.5.2

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)

## Warning: package 'rpart.plot' was built under R version 4.5.2

rpart.plot(arbol)

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

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%)