Refer to Table 11.13 on attitudes toward legalized abortion. For the response Y_t(1 = support legalization, 0 = oppose) for question t (t = 1, 2, 3) and for gender g (1 = female, 0 = male), consider the model logit[P(Y_t= 1)] = α + γg + β_twith β₃= 0.

a. A GEE analysis using unstructured working correlation gives correlation estimates 0.826 for questions 1 and 2, 0.797 for 1 and 3, and 0.832 for 2 and 3. What does this suggest about a reasonable working correlation structure?

b. Table 11.13 shows a GEE analysis with exchangeable working correlation. Interpret effects.

c. Treating the three responses for each subject as independent observations and performing ordinary logistic regression, β̂₁ = 0.149 (SE = 0.066), β̂₂ = 0.052 (SE = 0.066), and γ̂ = 0.004 (SE = 0.054). Give a heuristic explanation of why within-subject standard errors are much larger than with GEE, yet the between-subject standard error is smaller.

Table 11.13:

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Working Correlation Matrix Coll Col2 Col3 Rowl 1.0000 0.8173 0.8173 0.8173 Row2 1.0000 0.8173 Row3 0.8173 1.0000 0.8173 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Pr>|Z| Estimate Std Error Parameter 0.0637 Intercept -0.1253 0.0676 -1.85 question 1 question 2 question 3 0.1493 0.0297 5.02 <.0001 0.0520 0.0270 1.92 0.0544 0.0000 0.0000 female 0.0878 0.0034 0.04 0.9688