4. Let Y = political ideology (on an ordinal scale from 1 = very liberal to 5 = very conservative), x1 = gender (1 = female, 0 = male), x2 = political party (1 = Democrat, 0 = Republican).

(a) A main effects model with a cumulative logit link gives the output shown. Explain why the output reports four intercepts.

(b) Explain how to describe gender effect on political ideology with an odds ratio.

(c) Below is the results of LRT of the two explanotory vairables. What is the hypotheses to which the LRT for gender refers? And explain how to interpret the result of the test.

(d) When we add an interaction term to the model, we get the output shown. Explain how to find the estimated odds ratio for the gender effect on political ideology for Republicans.

(e) Using the interaction model, show how to find the estimated probability that a female Republican is in the first category (very liberal).