Introduction to Categorical Data Analysis

168 BUILDING AND APPLYING LOGISTIC REGRESSION MODELS
5.17 Refer to Table 2.10 on death penalty decisions. Fit a logistic model with the
two race predictors.
a. Test the model goodness of fit. Interpret.
b. Report the standardized residuals. Interpret.
c. Interpret the parameter estimates.
5.18 Table 5.12 summarizes eight studies in China about smoking and lung cancer.
a. Fit a logistic model with smoking and study as predictors. Interpret the
smoking effect.
b. Conduct a Pearson test of goodness of fit. Interpret.
c. Check residuals to analyze further the quality of fit. Interpret.
Table 5.12. Data for Problem 5.18 on Smoking and Lung Cancer
Lung Cancer Lung Cancer
City Smoking Yes No City Smoking Yes No
Beijing Yes 126 100 Harbin Yes 402 308
No 35 61 No 121 215
Shanghai Yes 908 688 Zhengzhou Yes 182 156
No 497 807 No 72 98
Shenyang Yes 913 747 Taiyuan Yes 60 99
No 336 598 No 11 43
Nanjing Yes 235 172 Nanchang Yes 104 89
No 58 121 No 21 36
Source: Based on data in Z. Liu, Int. J. Epidemiol., 21: 197–201, 1992. Reprinted by
permission of Oxford University Press.
5.19 Problem 7.9 shows a 2 × 2 × 6 table for Y = whether admitted to graduate
school at the University of California, Berkeley.
a. Set up indicator variables and specify the logit model that has department
as a predictor (with no gender effect) for Y = whether admitted (1 = yes,
0 = no).
b. For the model in (a), the deviance equals 21.7 with df = 6. What does this
suggest about the quality of the model fit?
c. For the model in (a), the standardized residuals for the number of females
who were admitted are (4.15, 0.50, −0.87, 0.55, −1.00, 0.62) for
Departments (1,2,3,4,5,6). Interpret.
d. Refer to (c). What would the standardized residual equal for the number of
males who were admitted into Department 1? Interpret.
e. When we add a gender effect, the estimated conditional odds ratio between
admissions and gender (1 = male, 0 = female) is 0.90. The marginal