Fit the adjacent-categories logit model (8.3.4) to Table 7.5, using scores {1,2,3,4} for income.

a. Test goodness of fit, and interpret the estimated effects of income and gender.

b. Perform a likelihood-ratio test of no income effect, controlling for gender, and interpret.

c. Fit the multicategory logit model that corresponds to loglinear model (GI, GS, IS). Does this model give a significantly better fit? Test the income- satisfaction association in this model, and compare results to (b).

d. Show that the logit model corresponding to loglinear model (S,IG), by which satisfaction is jointly independent of income and gender, seems to fit well. Argue that this is misleading because of sparseness and because it ignores ordering information. Show that an analysis that utilizes ordinality for the I-S association provides different conclusions.

e. Redo (a)-

(d) using scores {4, 10, 20, 30} that represent approximate income in thousands of dollars. Compare results.