"1. Problem 1 Part d) asks about estimating an odds ratio in the presence of an interaction. This is quite similar to problems discussed with respect to ordinary least squares (except we exponentiate the effect after we calculate it). However, Part e) asks for a confidence interval. For that we need the variance of the estimated effect (estimated log odds ratio). This is a weighted sum of coefficients. The following formula (contained in the book, but not so conveniently accessible) is useful for the variance of a weighted sum of correlated random variables. Call the random variables "B1" and "B2". The weights are real numbers denoted a1 and a2. Then:
Var(a1B1 + a2B2) = Var(B1)*(a1**2) + Var(B2)*(a2**2) + a1*a2*2*Cov(B1, B2)
The variances are listed on the diagonal of the estimated variance covariance matrix given on p. 683; the off-diagonal elements are the covariances. [
]2. Problem 3 Part a) asks about conditional vs. unconditional logistic regression. Conditional logistic regression is usually applied to paired or matched data (matching is a generalization of pairing). These data are not paired; however, conditional logistic regression can also be used to give more precise results when the sample size is small. I think that the authors are aiming at this second use here. [clearly]
3. Although Problem 3 Parts f) and g) ask you to calculate something similar to what you did in Problem 1 Part d), you aren't given the covariance matrix. Please skip these two parts of Problem 3. [while seemingly generous on his part, i'd like to point out that problem 3 has parts a through m!!]
Rick Chappell"
and now i hope you realize why i'm a wee bit worried about the qualifying exam.
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