Page 406 - Applied Statistics with R

406 CHAPTER 16. VARIABLE SELECTION AND MODEL BUILDING

best_aic_ind = which.min(hipcenter_mod_aic)
all_hipcenter_mod$which[best_aic_ind,]

## (Intercept) Age Weight HtShoes Ht Seated
## TRUE TRUE FALSE FALSE TRUE FALSE
## Arm Thigh Leg
## FALSE FALSE TRUE

Let’s fit this model so we can compare to our previously chosen models using
AIC and search procedures.

hipcenter_mod_best_aic = lm(hipcenter ~ Age + Ht + Leg, data = seatpos)

The extractAIC() function will calculate the AIC defined above for a fitted
model.
extractAIC(hipcenter_mod_best_aic)

## [1] 4.0000 274.2418

extractAIC(hipcenter_mod_back_aic)

## [1] 4.0000 274.2597

extractAIC(hipcenter_mod_forw_aic)

## [1] 4.0000 274.2418

extractAIC(hipcenter_mod_both_aic)

## [1] 4.0000 274.2418

We see that two of the models chosen by search procedures have the best possible
AIC, as they are the same model. This is however never guaranteed. We see
that the model chosen using backwards selection does not achieve the smallest
possible AIC.

plot(hipcenter_mod_aic ~ I(2:p), ylab = "AIC", xlab = "p, number of parameters",
pch = 20, col = "dodgerblue", type = "b", cex = 2,
main = "AIC vs Model Complexity")