Introduction to Categorical Data Analysis

240 LOGLINEAR MODELS FOR CONTINGENCY TABLES
7.14 Table 7.27, from a General Social Survey, relates responses on R = religious
service attendance (1 = at most a few times a year, 2 = at least several times
a year), P = political views (1 = Liberal, 2 = Moderate, 3 = Conservative),
B = birth control availability to teenagers between ages of 14 and 16 (1 =
agree, 2 = disagree), S = sexual relations before marriage (1 = wrong only
sometimes or not wrong at all, 2 = always or almost always wrong).
a. Find a loglinear model that fits these data well.
b. Interpret this model by estimating conditional odds ratios for each pair of
variables.
c. Consider the logistic model predicting (S) using the other variables as maineffect
predictors, without any interaction. Fit the corresponding loglinear
model. Does it fit adequately? Interpret the effects of the predictors on the
response, and compare to results from (b).
d. Draw the independence graph of the loglinear model selected in (a). Remark
on conditional independence patterns. For each pair of variables, indicate
whether the fitted marginal and conditional associations are identical.
Table 7.27. Data for Problem 7.14
Premarital Sex
1 2
Religious Attendence 1 2 1 2
Birth Control 1 2 1 2 1 2 1 2
1 99 15 73 25 8 4 24 22
Political views 2 73 20 87 37 20 13 50 60
3 51 19 51 36 6 12 33 88
Source: 1991 General Social Survey.
7.15 Refer to Table 7.13 in Section 7.4.5 on the substance use survey, which also
classified students by gender (G) and race (R).
a. Analyze these data using logistic models, treating marijuana use as the
response variable. Select a model.
b. Which loglinear model is equivalent to your choice of logistic model?
7.16 For the Maine accident data modeled in Section 7.3.2:
a. Verify that logistic model (7.9) follows from loglinear model (GLS, GI, LI,
IS).
b. Show that the conditional log odds ratio for the effect of S on I equals
βS 1 − βS 2 in the logistic model and λIS
11 + λIS
22 − λIS
12 − λIS
21 in the loglinear
model.