Model checking for count data: the folder risky.behavior contains data from a study of behavior of couples at risk for HIV; see Exercise 6.1. (a) Fit a Poisson regression model predicting number of...

Model checking for count data: the folder risky.behavior contains data from a study of behavior of couples at risk for HIV; see Exercise 6.1.

(a) Fit a Poisson regression model predicting number of unprotected sex acts from baseline HIV status. Perform predictive simulation to generate 1000 datasets and record both the percent of observations that are equal to 0 and the percent that are greater than 10 (the third quartile in the observed data) for each. Compare these values to the observed value in the original data.

(b) Repeat (a) using an overdispersed Poisson regression model.

(c) Repeat (b), also including ethnicity and baseline number of unprotected sex acts as input variables.