For the toxicity study of Table 12.9, collapsing to a binary response, consider linear logit models for the probability a fetus is normal.
a. Does the ordinary binomial model show evidence of overdispersion?
b. Fit the linear logit model using the quasi-likelihood approach with inflated binomial variance. How do the standard errors change?
c. Fit the linear logit model using quasi-likelihood with beta-binomial variance. Interpret and compare with previous results.
d. Fit the linear logit model using a GEE approach with exchangeable working correlation among fetuses in the same litter. Interpret and compare with previous results, including comparing the estimated GEE correlation with the estimate ρ̂ from part (c).
e. Fit the linear logit GLMM after adding a litter-specific normal random effect. Interpret and compare with previous results.
Table 12.9:
