Aula 11 - Regressão com Variável Dependente Binária
- Carregando dataset disponibilizado pela UCLA.
#Pacotes utilizados
pacotes <- c("rgl","car", "tidyverse",
"reshape2","jtools","lmtest","caret","pROC","ROCR","nnet")
if(sum(as.numeric(!pacotes %in% installed.packages())) != 0){
instalador <- pacotes[!pacotes %in% installed.packages()]
for(i in 1:length(instalador)) {
install.packages(instalador, dependencies = T)
break()}
sapply(pacotes, require, character = T)
} else {
sapply(pacotes, require, character = T)
}
## Loading required package: rgl
## Loading required package: car
## Loading required package: carData
## Loading required package: tidyverse
## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --
## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.4 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.0
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::recode() masks car::recode()
## x purrr::some() masks car::some()
## Loading required package: reshape2
##
## Attaching package: 'reshape2'
## The following object is masked from 'package:tidyr':
##
## smiths
## Loading required package: jtools
## Loading required package: lmtest
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: caret
## Loading required package: lattice
##
## Attaching package: 'caret'
## The following object is masked from 'package:purrr':
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## lift
## Loading required package: pROC
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
## Loading required package: ROCR
## Loading required package: nnet
## rgl car tidyverse reshape2 jtools lmtest caret pROC
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## ROCR nnet
## TRUE TRUE
link <- 'https://stats.idre.ucla.edu/wp-content/uploads/2016/02/sample.csv'
ucla <- read.csv(link)
glimpse(ucla)
## Rows: 200
## Columns: 6
## $ female <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ read <int> 57, 68, 44, 63, 47, 44, 50, 34, 63, 57, 60, 57, 73, 54,...
## $ write <int> 52, 59, 33, 44, 52, 52, 59, 46, 57, 55, 46, 65, 60, 63,...
## $ math <int> 41, 53, 54, 47, 57, 51, 42, 45, 54, 52, 51, 51, 71, 57,...
## $ hon <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1...
## $ femalexmath <int> 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
Calculando log-odds da variável dependente (hon)
- Regressão logística com apenas uma constante.
modelo1 <- glm(hon ~1,
data = ucla,
family = "binomial")
#visualizando os resultados
summ(modelo1, confint = T, digits = 3, ci.width = .95)
|
Observations
|
200
|
|
Dependent variable
|
hon
|
|
Type
|
Generalized linear model
|
|
Family
|
binomial
|
|
Link
|
logit
|
|
χ²(0)
|
-0.000
|
|
Pseudo-R² (Cragg-Uhler)
|
0.000
|
|
Pseudo-R² (McFadden)
|
0.000
|
|
AIC
|
224.710
|
|
BIC
|
228.008
|
|
|
Est.
|
2.5%
|
97.5%
|
z val.
|
p
|
|
(Intercept)
|
-1.125
|
-1.448
|
-0.803
|
-6.845
|
0.000
|
|
Standard errors: MLE
|
logLik(modelo1)
## 'log Lik.' -111.355 (df=1)
- Frequência da variável depedente (hon)
table(ucla$hon)
##
## 0 1
## 151 49
table(ucla$hon)/nrow(ucla)*100
##
## 0 1
## 75.5 24.5
- calculando a probabilidade
p <- 49/200
print(p)
## [1] 0.245
#ou transformar ou log odds em probabilidade de novo
p1 <- exp(-1.125)/ (1 + exp(-1.125))
print(p1)
## [1] 0.245085
- Calculando a chance (odds)
odds <- p/(1-p)
print(odds)
## [1] 0.3245033
log(odds)
## [1] -1.12546
Calculando Log odss manualmente
- chance (odds) dos homens estarem na categoria hon
#pertencer/ nao pertencer
odds_homens <- (17/ (74 + 17)) / (74/(74 + 17))
print(odds_homens)
## [1] 0.2297297
- chance (odds) das mulheres estarem na categoria hon
#pertencer/ nao pertencer
odds_mulheres <- (32/(32 + 77)) / (77/(32 + 77))
print(odds_mulheres)
## [1] 0.4155844
- Odds Mulheres / Odds Homens
odds_mulheres/odds_homens
## [1] 1.809015
#ou
(32*74)/(77*17)
## [1] 1.809015
- Intercepto = log odds homens
log(odds_homens)
## [1] -1.470852
- Beta_1 = log odds mulheres / odds homens
log(odds_mulheres/odds_homens)
## [1] 0.5927822
Regressão Logística Multivariada
\[logit(p) = log(p/(1-p))= β0 + β1*x1 + … + βk*x\]
modelo4 <- glm(hon ~ math + female + read,
data = ucla,
family = "binomial")
summ(modelo4, confint = T, digits = 3, ci.width = .95)
|
Observations
|
200
|
|
Dependent variable
|
hon
|
|
Type
|
Generalized linear model
|
|
Family
|
binomial
|
|
Link
|
logit
|
|
χ²(3)
|
66.540
|
|
Pseudo-R² (Cragg-Uhler)
|
0.421
|
|
Pseudo-R² (McFadden)
|
0.299
|
|
AIC
|
164.170
|
|
BIC
|
177.363
|
|
|
Est.
|
2.5%
|
97.5%
|
z val.
|
p
|
|
(Intercept)
|
-11.770
|
-15.123
|
-8.417
|
-6.880
|
0.000
|
|
math
|
0.123
|
0.062
|
0.184
|
3.931
|
0.000
|
|
female
|
0.980
|
0.154
|
1.806
|
2.324
|
0.020
|
|
read
|
0.059
|
0.007
|
0.111
|
2.224
|
0.026
|
|
Standard errors: MLE
|
logLik(modelo4)
## 'log Lik.' -78.08478 (df=4)