7.8 Somner (1982) reported on an Indonesian Children's Health Study designed to determine the effects of vitamin A deficiency in preschool children. The investigators were particularly interested in whether children with vitamin A deficiency were at increased risk of developing respiratory infection. Each child was measured at six times: 0, 3, 6, 9, 12, and 15 months. The following is a description of the variabes in the subset of the actual data set which is considered here: bage (baseline age in years), gender (gender = 1 if female and 0 if male), vita (vitamin A deficient = 1 if yes and = 0 if not), infect (respiratory infection = 1 if yes and 0 if not), and time (time of examination). The data is found in Somner.xls.

(a) Compute appropriate summary statistics for the response across the levels of the regressors and comment on some preliminary relationships that appear to exist.

(b) Fit a random intercept logistic model along with a random intercept and random slope logistic model and determine which is most appropriate via hypothesis testing.

(c) Produce an interaction plot involving vita and time and interpret.

(d) After removing nonsignificant terms, compute the estimated odds of a child developing a respiratory infection when he/she is vitamin A deficient. Do the same for children who are not vitamin A deficient and then construct the estimated odds ratio comparing the two groups. Interpret this estimated odds ratio.

(e) Characterize the children who seem to have the greatest chance of developing a respiratory infection.