Construct a generalized linear mixed-effects model for the Sexual Health study data with the fixed-effects component similar to that in Example9.7 and random slopes of the time effect and assess the model fit.

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Example 9.7 For longitudinal data analysis, a primary interest is to assess temporal changes. For ex- ample, we would like to compare the HIV knowledge score changes in the Sexual Health study. One would expect that the knowledge will increase as time goes on, and our initial exploratory analysis confirms such a temporal trend (see Figure 9.1). However, since only the intervention group was delivered educational information regarding the transmission and prevention of HIV, we would like to know if there are any differences between the two groups. Let z; be the treatment indicator (=1 for intervention and = 0 for control group). We use it, t = 1, 2, to index the time; at the baseline (t = 1), x = 0 and at 3 months post treatment (t 2), 12 = 1. Consider the following marginal model for the HIV knowledge