3. Refer to Agresti’s Table 9.8 (p. 289). This is the Harvard study on children’s respiratory illness measured at ages 7-10. Here age and maternal smoking status are treated as predictors. The data is provided in SAS format (resp).
(a) (15 pts) Analyze the data using the marginal GEE model with several di?erent working correlation structures (e.g., independent, AR1 or exchangeable), including age, maternal smoking status and the interaction term of age and maternal smoking status. Compare the estimators, standard errors and p-values using different working correlation structures. Are any of the predictors signi?cant?
(b) (5 pts) Based on the Pearson correlation from the sample residuals, which working correlation matrix is closer to the sample correlation matrix?
(c) (15 pts) Analyze the data using the generalized linear mixed model with random intercept only. Report the estimators, standard errors and p-values. Test whether the variance component is signi?cant.
(d) (15 pts) Analyze the data using the generalized linear mixed model with random intercept and random slope for maternal smoking. Report the estimators, standard errors and p-values. Test whether the variance components are signi?cant. (Note: it might take some time to get the ?nal convergence in SAS).
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