Introduction to Categorical Data Analysis

PROBLEMS 239
Table 7.25. Opinions about Government Spending
Cities 1 2 3
Law Enforcement 1 2 3 1 2 3 1 2 3
Environment Health
1 1 62 17 5 90 42 3 74 31 11
2 11 7 0 22 18 1 19 14 3
3 2 3 1 2 0 1 1 3 1
2 1 11 3 0 21 13 2 20 8 3
2 1 4 0 6 9 0 6 5 2
3 1 0 1 2 1 1 4 3 1
3 1 3 0 0 2 1 0 9 2 1
2 1 0 0 2 1 0 4 2 0
3 1 0 0 0 0 0 1 2 3
Source: 1989 General Social Survey; 1 = too little, 2 = about right, 3 = too much.
which has estimated SE = 0.523. Show that a 95% confidence interval for
the true odds ratio equals (3.1, 24.4). Interpret.
c. Estimate the conditional odds ratios using the “too much” and “too little”
categories for each of the other pairs of variables. Summarize the
associations. Based on these results, which term(s) might you consider
dropping from the model? Why?
Table 7.26. Output for Fitting Model to Table 7.25
Criteria For Assessing Goodness Of Fit
Criterion DF Value
Deviance 48 31.6695
Pearson Chi-Square 48 26.5224
Standard Standard
Parameter DF Estimate Error Parameter DF Estimate Error
e*h 1 1 1 2.1425 0.5566 h*c 1 1 1 −0.1865 0.4547
e*h 1 2 1 1.4221 0.6034 h*c 1 2 1 0.7464 0.4808
e*h 2 1 1 0.7294 0.5667 h*c 2 1 1 −0.4675 0.4978
e*h 2 2 1 0.3183 0.6211 h*c 2 2 1 0.7293 0.5023
e*l 1 1 1 −0.1328 0.6378 h*l 1 1 1 1.8741 0.5079
e*l 1 2 1 0.3739 0.6975 h*l 1 2 1 1.0366 0.5262
e*l 2 1 1 −0.2630 0.6796 h*l 2 1 1 1.9371 0.6226
e*l 2 2 1 0.4250 0.7361 h*l 2 2 1 1.8230 0.6355
e*c 1 1 1 1.2000 0.5177 c*l 1 1 1 0.8735 0.4604
e*c 1 2 1 1.3896 0.4774 c*l 1 2 1 0.5707 0.4863
e*c 2 1 1 0.6917 0.5605 c*l 2 1 1 1.0793 0.4326
e*c 2 2 1 1.3767 0.5024 c*l 2 2 1 1.2058 0.4462