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 table, collapsed over department, has odds ratio 1.84. Explain how these associations differ so much for these data.
Problem 7.9
Table 7.23 refers to applicants to graduate school at the University of California, Berkeley for the fall 1973 session. Admissions decisions are presented by gender of applicant, for the six largest graduate departments. Denote the three variables by A = whether admitted, G = gender, and D = department. Fit loglinear model (AD,AG,DG).
a. Report the estimated AG conditional odds ratio, and compare it with the AG marginal odds ratio. Why are they so different?
b. Report G2 and df values, and comment on the quality of fit. Conduct a residual analysis. Describe the lack of fit.
c. Deleting the data for Department 1, re-fit the model. Interpret.
d. Deleting the data for Department 1 and treating A as the response variable, fit an equivalent logistic model for model (AD,AG,DG) in (c). Show how to use each model to obtain an odds ratio estimate of the effect of G on A,
