Poisson regression: the folder risky.behavior contains data from a randomized trial targeting couples at high risk of HIV infection. The intervention provided counseling sessions regarding practices that could reduce their likelihood of contracting HIV. Couples were randomized either to a control group, a group in which just the woman participated, or a group in which both members of the couple participated. One of the outcomes examined after three months was “number of unprotected sex acts.”
(a) Model this outcome as a function of treatment assignment using a Poisson regression. Does the model fit well? Is there evidence of overdispersion?
(b) Next extend the model to include pre-treatment measures of the outcome and the additional pre-treatment variables included in the dataset. Does the model fit well? Is there evidence of overdispersion?
(c) Fit an overdispersed Poisson model. What do you conclude regarding effectiveness of the intervention?
(d) These data include responses from both men and women from the participating couples. Does this give you any concern with regard to our modeling assumptions?
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