Introduction to Categorical Data Analysis

PROBLEMS 233
7.2 For the saturated model with Table 2.1, software reports the {ˆλ XY
ij } estimates:
Parameter DF Estimate Std Error
gender*belief females yes 1 0.1368 0.1507
gender*belief females no 0 0.0000 0.0000
gender*belief males yes 0 0.0000 0.0000
gender*belief males no 0 0.0000 0.0000
Show how to use these to estimate the odds ratio.
7.3 Table 7.17 is from a General Social Survey. White subjects in the sample were
asked: (B) Do you favor busing (Negro/Black) and white school children from
one school district to another?, (P ) If your party nominated a (Negro/Black)
for President, would you vote for him if he were qualified for the job?, (D)
During the last few years, has anyone in your family brought a friend who
was a (Negro/Black) home for dinner? The response scale for each item was
(1 = Yes, 2 = No or Do not know). Table 7.18 shows output from fitting model
(BD, BP, DP). Estimates equal 0 at the second category for any variable.
Table 7.17. Data for Problem 7.3
Home
President Busing 1 2
1 1 41 65
2 72 175
2 1 2 9
2 4 55
Source: 1991 General Social Survey, with categories 1 = yes, 2 =
no or do not know.
a. Analyze the model goodness of fit. Interpret.
b. Estimate the conditional odds ratios for each pair of variables. Interpret.
c. Show all steps of the likelihood-ratio test for the BP association, including
explaining which loglinear model holds under the null hypothesis. Interpret.
d. Construct a 95% confidence interval for the BP conditional odds ratio.
Interpret.
7.4 In a General Social Survey respondents were asked “Do you support or oppose
the following measures to deal with AIDS? (1) Have the government pay all of
the health care costs of AIDS patients; (2) develop a government information
program to promote safe sex practices, such as the use of condoms.” Table 7.19
shows responses on these two items, classified also by the respondent’s gender.