Page 435 - Applied Statistics with R

17.3. WORKING WITH LOGISTIC REGRESSION 435

select a subset of predictors, we can use a stepwise procedure as we did with
ordinary linear regression. Recall that AIC and BIC were defined in terms
of likelihoods. Here we demonstrate using AIC with a backwards selection
procedure.

chd_mod_selected = step(chd_mod_additive, trace = 0)
coef(chd_mod_selected)

## (Intercept) tobacco ldl famhistPresent typea
## -6.44644451 0.08037533 0.16199164 0.90817526 0.03711521
## age
## 0.05046038

We could again compare this model to the additive models.

∶ sbp = adiposity = obesity = alcohol = 0
0
anova(chd_mod_selected, chd_mod_additive, test = "LRT")

## Analysis of Deviance Table
##
## Model 1: chd ~ tobacco + ldl + famhist + typea + age
## Model 2: chd ~ sbp + tobacco + ldl + adiposity + famhist + typea + obesity +
## alcohol + age
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 456 475.69
## 2 452 472.14 4 3.5455 0.471

Here it seems that we would prefer the selected model.

17.3.5 Confidence Intervals

We can create confidence intervals for the parameters using the confint()
function as we did with ordinary linear regression.

confint(chd_mod_selected, level = 0.99)

## Waiting for profiling to be done...

## 0.5 % 99.5 %
## (Intercept) -8.941825274 -4.18278990
## tobacco 0.015704975 0.14986616