Regresión con efectos fijos

Preparación del ambiente de trabajo

library(ggplot2)
library(dplyr)
library(broom)
set.seed(2025)

---

Simulación y exploración de datos

n <- 200
x1 <- rnorm(n)
x2 <- sample(c("A", "B"), n, replace = TRUE)
prob <- 1 / (1 + exp(-(0.5 * x1 + ifelse(x2 == "B", 1, 0))))
y <- rbinom(n, 1, prob)

df <- data.frame(y = as.factor(y), x1 = x1, x2 = as.factor(x2))

ggplot(df, aes(x = x1, fill = y)) +
  geom_density(alpha = 0.5) +
  facet_wrap(~x2) +
  labs(title = "Distribución de x1 por clase y y categoría x2")

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Ajuste del modelo de regresión logística

modelo_logit <- glm(y ~ x1 + x2, data = df, family = "binomial")
summary(modelo_logit)

## 
## Call:
## glm(formula = y ~ x1 + x2, family = "binomial", data = df)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.1209     0.2036   0.594 0.552669    
## x1            0.6034     0.1649   3.659 0.000253 ***
## x2B           0.9121     0.3142   2.903 0.003695 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 265.63  on 199  degrees of freedom
## Residual deviance: 242.18  on 197  degrees of freedom
## AIC: 248.18
## 
## Number of Fisher Scoring iterations: 4

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Evaluación del modelo

df$prob_pred <- predict(modelo_logit, type = "response")
df$y_pred <- ifelse(df$prob_pred > 0.5, 1, 0)

table(Predicho = df$y_pred, Real = df$y)

##         Real
## Predicho   0   1
##        0  29  21
##        1  47 103

ggplot(df, aes(x = prob_pred, fill = y)) +
  geom_histogram(bins = 30, position = "identity", alpha = 0.6) +
  labs(title = "Distribución de probabilidades predichas")

---

Interpretación de coeficientes

broom::tidy(modelo_logit, exponentiate = TRUE, conf.int = TRUE)

## # A tibble: 3 × 7
##   term        estimate std.error statistic  p.value conf.low conf.high
##   <chr>          <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
## 1 (Intercept)     1.13     0.204     0.594 0.553       0.758      1.69
## 2 x1              1.83     0.165     3.66  0.000253    1.33       2.55
## 3 x2B             2.49     0.314     2.90  0.00369     1.36       4.66