Refer to the previous exercise and the Mental data file.

a. For the main effects fit, summarize the life events effect with probability interpretations for P(Y = 1) analogous to those given in the text for P(Y = 4).

b. Find and interpret the estimate of R2 and the multiple correlation for the corresponding latent variable model.

c. Compare the estimated effects to those obtained after combining response categories 3 and 4. What property of the model does this reflect?

d. Since n = 40 is not large, the choice of prior distribution in a Bayesian analysis can be influential. Illustrate this by repeating the analysis of Section 6.3.9 using

σ = 1 in the normal priors. Compare to the results with σ = 10.