A cumulative logit model is fitted to data from a General Social Survey, with Y = political ideology (very liberal to very conservative) and x = religious preference (Protestant, Catholic, Jewish,...

A cumulative logit model is fitted to data from a General Social Survey, with Y = political ideology (very liberal to very conservative) and x = religious preference (Protestant, Catholic, Jewish, Other). With indicator variables for the first three religion categories, the ML fit has αˆ1 = −1.03, αˆ2 = −0.13, αˆ3 = 1.57, αˆ4 = 2.41, βˆ1 = −1.27, βˆ2 = −1.22, βˆ3 = −0.44.

a. How many categories does Y have? Which group is estimated to be the (i) most liberal, (ii) most conservative?

b. Use an estimated odds ratio to compare political ideology for the Protestant and Catholic groups. Interpret.