For the DOS data set, fit a cumulative logit model with the three-level depression diagnosis as the ordinal response and Age, Gender, CIRS, and MS as covariates.

(a) Repeat the analyses (a), (b), and (c) in Problem5.6

(b) Test whether the equal slopes assumption is true.

(c) Based on the equal slope assumption, test the linear hypothesis: \(\mathrm{H}_{0}: \beta_{\text {Age }}=1\) vs. \(\mathrm{H}_{a}: \beta_{\text {Age }} eq 1\) and explain your results. Note that the above is not a linear contrast, and thus you may use an offset term.

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5.6 For the DOS data set, treat the three-level depression diagnosis as a nominal outcome, and compare the results. (a) Fit a generalized logistic model with the three-level depression diagnosis as the response and Age, Gender, CIRS, and MS as covariates. How does the model fit the data? Explain your results. (b) What is the estimated probability ratio of major depression of a widowed male with Age 75 and CIRS = 15 to a married female at the same Age but CIRS = 10? Explain your results. (c) Based on the parameter estimates, compute the odds ratio of being depressed (major and minor depression) vs. nondepression between males and females (other characteristics such as Age, CIRS, and MS are holding constant). Ex- plain your results. (d) Fit a multinomial probit model and repeat the analyses (a), (b), and (c) above.