9.5 Table 9.7 provides data (obtained from Michael Friendly’s web site at York University)

pertaining to the relationship between a treatment for diabetes (treated or placebo), sex

(male or female), and improvement status (improved or not improved).

a. Fit the logistic regression model to predict improvement status from treatment, sex, and their interaction. Use the likelihood ratio test to test the interaction between treatment and sex. Report and fully interpret the results from a substantive perspective.

b. If one were to fit a log-linear model using all three variables (improvement, treatment, and sex), what model comparison would be equivalent to the one performed in part (a)? Explain why these model comparisons are conceptually equivalent: What does the model comparison represent in each case (logistic/log-linear)?

c. Fully interpret all of the parameter estimates in the logistic regression model that contains only the main effects of treatment and sex (i.e., with no interaction).

d. What log-linear model is equivalent to the logistic regression model fit in part (c)?

Fit this log-linear model and show which of its parameter estimates are equivalent to those obtained from the logistic regression model in part (c).

e. Based on the logistic regression model with the interaction between treatment and sex, what is the predicted probability that a treated male would improve? What is this predicted probability from the model without the interaction term?