8.28 For matched pairs, to obtain conditional ML { j } for model (8.5) using software for ordinary logistic regression, let Let x

8.28 For matched pairs, to obtain conditional ML { ˆ βj } for model (8.5) using software for ordinary logistic regression, let

Let x ∗
1i = x ∗
1i1 − x ∗
1i2, . . . , x ∗
ki = x ∗
ki1 − x ∗
ki2. Fit the ordinary logistic model to y ∗ with predictors {x ∗
1 , . . . , x ∗
k }, forcing the intercept parameter α to equal zero.
This works because the likelihood is the same as the conditional likelihood for model (8.5) after eliminating {αi }.

a. Apply this approach to model (8.4) with Table 8.1 and report ˆ β and its SE.

b. The pairs (yi1 = 1, yi2 = 1) and (yi1 = 0, yi2 = 0) do not contribute to the likelihood or to estimating {βj }. Identify the counts for such pairs in Table 8.1. Do these counts contribute to McNemar’s test?

y = 1 when (y1 = 1, yi2 = 0), y = 0 when (y1 = 0, yi2 = 1)