Refer to the example in Section 8.1.4.

a. Using the fitted model, estimate the probability of response "no" for black females, (i) using parameter estimates, (ii) using fitted values.

b. Fit the logit model for which race has no effect on belief in an afterlife, con- trolling for gender. Test the goodness of fit, and interpret. Which loglinear model is equivalent to this model?

c. Describe the gender effect for the model in

(b) by reporting the estimated odds ratio for each pair of response categories. Interpret, and explain how these relate to the marginal gender-belief odds ratios.

d. Does the model in

(b) imply that race and belief in an afterlife are marginally independent, collapsing over gender? (Hint: Consider collapsibility for the corresponding loglinear model.)