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

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?

f. Provide SAS coding.

Table 5.9 is attached to this email and to access the horseshoe crab data: http://www.stat.ufl.edu/~aa/intro-cda/appendix.html

When you click on the link, look for the bold headline "A.6 SAS file for analyses of horseshoe crab data in Table 3.2 of 2nd edition (Table 4.2 of first edition)