Model selection

Building Response Models in R

Kathrin Gruber

Assistant Professor of Econometrics Erasmus University Rotterdam

Extending the logistic response model (1)

summary(choice.data[c("FEAT.HOP","DISPL.HOP","FEATDISPL.HOP")])

    FEAT.HOP         DISPL.HOP       FEATDISPL.HOP     
 Min.   :0.00000   Min.   :0.00000   Min.   :0.000000  
 1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.000000  
 Median :0.00000   Median :0.00000   Median :0.000000  
 Mean   :0.03645   Mean   :0.03538   Mean   :0.009292  
 3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.000000  
 Max.   :1.00000   Max.   :1.00000   Max.   :1.000000

Extending the logistic response model (2)

extended.model <- glm(HOPPINESS ~ price.ratio + 
                      DISPL.HOP + FEAT.HOP + FEATDISPL.HOP, 
                      family = binomial, data  = choice.data)

margins(extended.model)

 price.ratio DISPL.HOP FEAT.HOP FEATDISPL.HOP
    -0.4471  0.009486  0.04973        0.1086

Summarizing the model

extended.model <- glm(HOPPINESS ~ price.ratio + 
                      DISPL.HOP + FEAT.HOP + FEATDISPL.HOP, 
                      family = binomial, data  = choice.data)
summary(extended.model)

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)    -3.6250     0.1447 -25.053  < 2e-16 ***
price.ratio    -6.6663     0.4127 -16.154  < 2e-16 ***
DISPL.HOP       0.1415     0.2599   0.544 0.586204    
FEAT.HOP        0.7415     0.3780   1.962 0.049806 *  
FEATDISPL.HOP   1.6189     0.4789   3.381 0.000723 ***

    Null deviance: 1820.0  on 2797  degrees of freedom
Residual deviance: 1275.8  on 2793  degrees of freedom
AIC: 1285.8

The deviance principle

null.model <- glm(HOPPINESS ~ 1, family = binomial, data = choice.data)
anova(extended.model, null.model, test = "Chisq")

Analysis of Deviance Table

Model 1: HOPPINESS ~ 1
Model 2: HOPPINESS ~ price.ratio + DISPL.HOP + FEAT.HOP + FEATDISPL.HOP
  Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
1      2797     1820.0                          
2      2793     1275.8  4   544.23 < 2.2e-16 ***

Eliminating predictors

final.model <- stepAIC(extended.model, direction = "backward", trace = FALSE)
summary(final.model)

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)    -3.6268     0.1450 -25.018  < 2e-16 ***
price.ratio    -6.7167     0.4033 -16.655  < 2e-16 ***
FEAT.HOP        0.7327     0.3780   1.938 0.052577 .  
FEATDISPL.HOP   1.6041     0.4789   3.349 0.000811 ***

    Null deviance: 1820.0  on 2797  degrees of freedom
Residual deviance: 1276.1  on 2794  degrees of freedom
AIC: 1284.1

Let's practice!

Building Response Models in R