Table 9.17 summarizes a study with variables age of mother (A), length of gestation (G) in days, infant survival (I), and number of cigarettes smoked per day during the prenatal period (S). Treat G and I as response variables and A and S as explanatory.

a. Explain why a loglinear model should include the λ^AS term.

b. Fit the models (AGIS), (AGI, AIS, AGS, GIS), (AG, AI, AS, GI, GS, IS), and (AS, G, I). Identify a subset of models nested between two of these that may fit well. Select one such model.

Table 9.17:

Infant Survival Smoking Gestation Yes No Age 315 4012 40 459 < 260 > 260 < 260 < 30 50 24 260 41 14 30 + s 260 > 260 147 1594 1594 11 s 260 > 260 124