Refer to the subject-specific modelfor binary matched pairs.
a. Show that exp(β) is a conditional odds ratio between observation and outcome. Explain the distinction between it and the odds ratio exp(β) for model.
b. Using the conditional distribution, show that = log(n21/n12).
c. For a random sample of n pairs, explain why
Similarily, state E(n12/n). Usipng their ratio for fixed n and as n →∞ explain why n21/n12 exp(β).
d. Show that the Mantel-Haenszel estimator of a common odds ratio in the 2×2×n form of the data simplifies to exp(= n21/n12 .
e. Use the delta method to show(10.10.for the SE of .
f. For a table of the form shown in Table 10.2, show that the CMH statistic is algebraically identical to the McNemar statistic (n21-n12)2/(n21 +n12)for tables of Table 10.1 type.
Rating of Performance of Prime Minister
First
Second Survey
Total
Survey
Approve Disapprove
Approve
794
150
944
Disapprove
86
570
656
Total
880
720
1600
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