Regresión Logística - Titanic

Teoría

La regresión logística es un modelo estadístico de clasificación binaria, que estima la probabilidad de que ocurra un evento (valor 1) frente a que no ocurra (valor 0), en función de variables independientes. # Instalar paquetes y llamar librerías

# install.packages("titanic")
library(readr)
titanic <- read_csv("~/Conexión de interfaces/Conexión de interfaces/titanic.csv")

## Rows: 1310 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (7): name, sex, ticket, cabin, embarked, boat, home.dest
## dbl (7): pclass, survived, age, sibsp, parch, fare, body
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

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

## Loading required package: ggplot2
## Loading required package: lattice

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

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ stringr   1.5.1
## ✔ forcats   1.0.0     ✔ tibble    3.3.0
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.1.0     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ purrr::lift()   masks caret::lift()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Crear la base de datos

df <- titanic

Entender la base de datos

summary(df)

##      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(df)

## spc_tbl_ [1,310 × 14] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ pclass   : num [1:1310] 1 1 1 1 1 1 1 1 1 1 ...
##  $ survived : num [1:1310] 1 1 0 0 0 1 1 0 1 0 ...
##  $ name     : chr [1:1310] "Allen, Miss. Elisabeth Walton" "Allison, Master. Hudson Trevor" "Allison, Miss. Helen Loraine" "Allison, Mr. Hudson Joshua Creighton" ...
##  $ sex      : chr [1:1310] "female" "male" "female" "male" ...
##  $ age      : num [1:1310] 29 0.917 2 30 25 ...
##  $ sibsp    : num [1:1310] 0 1 1 1 1 0 1 0 2 0 ...
##  $ parch    : num [1:1310] 0 2 2 2 2 0 0 0 0 0 ...
##  $ ticket   : chr [1:1310] "24160" "113781" "113781" "113781" ...
##  $ fare     : num [1:1310] 211 152 152 152 152 ...
##  $ cabin    : chr [1:1310] "B5" "C22 C26" "C22 C26" "C22 C26" ...
##  $ embarked : chr [1:1310] "S" "S" "S" "S" ...
##  $ boat     : chr [1:1310] "2" "11" NA NA ...
##  $ body     : num [1:1310] NA NA NA 135 NA NA NA NA NA 22 ...
##  $ home.dest: chr [1:1310] "St Louis, MO" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" "Montreal, PQ / Chesterville, ON" ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   pclass = col_double(),
##   ..   survived = col_double(),
##   ..   name = col_character(),
##   ..   sex = col_character(),
##   ..   age = col_double(),
##   ..   sibsp = col_double(),
##   ..   parch = col_double(),
##   ..   ticket = col_character(),
##   ..   fare = col_double(),
##   ..   cabin = col_character(),
##   ..   embarked = col_character(),
##   ..   boat = col_character(),
##   ..   body = col_double(),
##   ..   home.dest = col_character()
##   .. )
##  - attr(*, "problems")=<externalptr>

df <- df[, c("survived", "pclass","sex","age")]
df <- na.omit(df)
df$survived <- as.factor(df$survived)
df$pclass <- as.factor(df$pclass)
df$sex <- as.factor(df$sex)

Crear el modelo

modelo <- glm(survived ~ ., data=df, family=binomial)
summary(modelo)

## 
## Call:
## glm(formula = survived ~ ., family = binomial, data = df)
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  3.522074   0.326702  10.781  < 2e-16 ***
## pclass2     -1.280570   0.225538  -5.678 1.36e-08 ***
## pclass3     -2.289661   0.225802 -10.140  < 2e-16 ***
## sexmale     -2.497845   0.166037 -15.044  < 2e-16 ***
## age         -0.034393   0.006331  -5.433 5.56e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1414.62  on 1045  degrees of freedom
## Residual deviance:  982.45  on 1041  degrees of freedom
## AIC: 992.45
## 
## Number of Fisher Scoring iterations: 4

Probar el modelo

prueba <- data.frame(pclass=as.factor(c(1,3)),
sex=as.factor(c("female","male")),age=c(25,40))
probabilidad <- predict(modelo, newdata=prueba, type="response")
cbind(prueba, probabilidad_sobrevive=probabilidad)

##   pclass    sex age probabilidad_sobrevive
## 1      1 female  25             0.93476160
## 2      3   male  40             0.06653593

Conclusiones

• Ser hombre reduce fuertemente la probabilidad de sobrevivir, con un coeficiente de aproximadamente -2.50.

• Clase también pesa mucho: frente a 1ª clase, estar en 2ª baja la supervivencia, con un coeficiente de. -1.28 y en 3ª baja todavía más con el coeficiente: -2.29.

• Edad tiene igualmente un efecto negativo pero más gradual, ya que por cada año extra, la probabilidad tiende a disminuir un -0.034.

Considerando todos esos efectos, el modelo predice lo siguiente: una mujer de 25 años ubicada en 1ª clase cuenta con un 0.935 de probabilidad de sobrevivir, mientras un hombre, de 40 años y 3ª clase cuenta con una probabilidad de 0.067.