6.9 A cumulative logit model is fitted to data from the 2004 General Social Survey, with Y = political ideology (extremely liberal or liberal, slightly liberal, moderate, slightly conservative, extremely conservative or conservative)

and predictor religious preference (Protestant, Catholic, Jewish, None).

With indicator variables for the first three religion categories, the ML fit has

ˆα

1 = −1.03, ˆα2 = −0.13, ˆα3 = 1.57, ˆα4 = 2.41, ˆ β1 = −1.27, ˆ β2 = −1.22,

ˆ β3 = −0.44.

a. Why are there four { ˆαj }?Why is ˆα1 < ˆα2 < ˆα3 < ˆα4?

b. Which group is estimated to be the (i) most liberal, (ii) most conservative?

Why?

c. Estimate the probability of the most liberal response for the Protestant and None groups.

d. Use an estimated odds ratio to compare political ideology for the (i) Protestant and None groups, (ii) Protestant and Catholic groups.