5.3 For the horseshoe crab data with width, color, and spine as predictors, suppose you start a backward elimination process with the most complex model possible.

Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction. Table 5.9 shows the fit for this model and various simpler models.

a. Conduct a likelihood-ratio test comparing this model to the simpler model that removes the three-factor interaction term but has all the two-factor interactions. Does this suggest that the three-factor term can be removed from the model?

b. At the next stage, if we were to drop one term, explain why we would select model C ∗ S + C ∗ W.

c. For the model at this stage, comparing to the model S + C ∗ W results in an increased deviance of 8.0 on df = 6 (P = 0.24); comparing to the model W + C ∗ S has an increased deviance of 3.9 on df = 3 (P = 0.27). Which term would you take out?

d. Finally, compare the working model at this stage to the main-effects model C + S + W. Is it permissible to simplify to this model?

e. Of the models shown in the table, which is preferred according to the AIC?