In this question we develop a regression model to assess the treatment effect for stigma in the DTS study, controlling for demographics and baseline measurements. We will use the cumulative logit link functions for the four-level stigma outcome and apply some model selection criteria to trim the independent variables.

(a) Perform the backwards model selection for marginal models using treatment, visit time, age, gender, marriage status, education, baseline HamD, baseline TS, and CIRS as covariates, with the elimination threshold for p-values set at \(20 \%\). Treat treatment, gender, marriage status, and baseline TS as categorical and the others as continuous variables. Since the purpose is to assess treatment effect, which occurs over time, treatment and its interaction with time will be kept in the model. Summarize the selection process (which factors are eliminated at each step and why).

(b) Is there a significant treatment effect based on the model obtained in part (a)?

(c) For the marginal model in part (a), identify subjects with the most influence on the coefficient of the interaction of treatment effects and time.

(d) Based on the marginal model obtained in part (a), develop a generalized mixedeffects model using the same fixed-effects and adding a random intercept. Is there significant treatment effect based on the generalized mixed-effects model?

(e) Identify subjects with the most influence on the estimate of treatment effects based on the model in part (d). Compare the results with those from part (c).