Refer to Table 7.5. Treating job satisfaction as the response, analyze the data using a model with cumulative logits.

a. Test the fit, and describe the effect of income.

b. Conduct a likelihood-ratio test for the effect of income, controlling for gender, and interpret. Compare results to those for the test about this effect in Sections 7.3.4 and 7.3.5. Does it help to utilize the ordinality of income and satisfaction?

c. Compare the estimated effect of income to the estimate obtained by com- bining categories "Very dissatisfied" and "A little satisfied." What property of the proportional odds model does this reflect?

d. Can gender be dropped from the model? Interpret the effect of income on satisfaction for this simpler model.