Table 5.15 describes results from a study in which subjects received a drug and the outcome measures whether the subject became incontinent (y = 1, yes; y = 0, no). The three explanatory variables are lower urinary tract variables that represent drug-induced physiological changes.
a. Report the prediction equations when each predictor is used separately in logistic regressions.
b. Try to fit a main-effects logistic regression model containing all three predictors. What does your software report for the effects and their standard errors? (The ML estimates are actually -∞ for x1 and x2 and ∞ for x3.)
c. Use conditional logistic regression to find an exact P-value for testing H0: β3 = 0. [The exact distribution is degenerate, and neither ordinary ML or exact conditional ML works with these data. For alternative approaches, see articles by D. M. Potter (Statist. Med., 24: 693-708, 2005) and G. Heinze and M. Schemper (Statist. Med., 22: 1409-1419, 2002).]
