An Introduction to Categorical Data Analysis

3rd Addition

Alan Agresti

7.5

7.5 Refer to the auto accident injury data shown in Table 7.5. a. Explain why the fitted odds ratios in Table 7.7 for model (GL, GS, LS, GI, LI, SI) suggest that the most likely case for injury is accidents for females not wearing seat belts in rural locations. b. Consider the following two-stage model. The first stage is a logistic model with S as the response, for the three-way G x L x S table. The second stage is a logistic model with these three variables as predictors for / in the four-way table. Explain why this composite model is sensible, fit the models, and interpret results.lable 7.5 shows results of accidents in the state of Maine for 06,094 passengers in an and light trucks. The table classifies passengers by gender (G), location of accident (f's seat-belt use (S), and injury (1). The table reports the sample proportion of passengers wh were injured. For each GL combination, the proportion of injuries was about halved passengers wearing seat-belts. Table 7.5 Injury (1) by gender (G), location (L), and seat-belt use (S), with fit of loglinear mod (GLS, GI, LI, SD). Seat Injury (GLS, GI, LI, SD) Gender Location Belt No Yes No Yes Sample Prop. Yes Female Rural No 3246 973 3254.7 964.3 Yes 6134 757 6093.5 797.5 0.23 Urban No 7287 996 7273.2 1009.8 0.11 Yes 11587 759 11632.6 713.4 0.12 0.06 Male Rural No 6123 1084 6150.2 1056.8 Yes 6693 513 6697.6 0.15 508.4 Urban No 10381 812 10358.9 0.07 834.1 Yes 10969 380 0.07 10959.2 389.8 0.03 Source: I am grateful to Dr. Cristanna Cook, Medical Care Development, Augusta, Maine, for supplying these data, which are in the Accidents2 data file at the text website