9.3 Refer to the previous exercise. Further study shows evidence of an interaction between gender and substance type. Using GEE with exchangeable working correlation, the estimated probability ˆπ of using a particular substance satisfies logit(πˆ ) = −0.57 + 1.93S1 + 0.86S2 + 0.38R − 0.20G + 0.37G × S1

+ 0.22G × S2 where R,G, S1, S2 are dummy variables for race (1 = white, 0 = nonwhite), gender (1 = female, 0 = male), and substance type (S1 = 1, S2 = 0 for alcohol;

S1 = 0, S2 = 1 for cigarettes; S1 = S2 = 0 for marijuana). Show that:

a. The group with highest estimated probability of use of marijuana is white males. What group is it for alcohol?

b. Given gender, the estimated odds a white subject used a given substance are 1.46 times the estimated odds for a nonwhite subject.

c. Given race, the estimated odds a female has used alcohol are 1.19 times the estimated odds for males; for cigarettes and for marijuana, the odds ratios are 1.02 and 0.82.

d. Given race, the estimated odds a female has used alcohol (cigarettes) are 9.97 (2.94) times the estimated odds she has used marijuana.

e. Given race, the estimated odds a male has used alcohol (cigarettes) are 6.89 (2.36) times the estimated odds he has used marijuana. Interpret the interaction.