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Chapter 21
merely the ratios ofthe exponentiated parameter estimates. For example, the cumulativeodds
ratio for 18–30 vs. >60 is 1.00/0.723 = 1.383.
Figure 21-12
Odds ratios for driving frequency
This table displays thecumulative odds ratios for the factor levels of Driving frequency,using
10–14,999 miles/yearas the reference category. SinceDriving frequency is not involved in any
interaction terms, the odds ratiosare merely the ratios of the exponentiated parameter estimates.
For example, the cumulative odds ratio for 20–29,999 miles/year vs. 10–14,999 miles/year is
0.101/0.444 = 0.227.
Generalized Cumulative Model
Figure 21-13
Testof parallel lines
The test of parallel lines can help you assess whetherthe assumption that the parameters are the
same for all response categories is reasonable. This test compares the estimated model with one
set of coefficientsfor all categories to a generalized model with a separate set of coefficients for
each category.
The WaldFtest is an omnibus test of the contrast matrix for the parallel lines assumption that
provides asymptotically correctpvalues; forsmall to mid-sized samples, the adjusted Wald F
statistic performs well. The significance value is near 0.05, suggesting that the generalized model
maygiveanimprovementinthemodelfit;however, the Sequential Sidakadjusted test reports a
significance value high enough (0.392) that, overall, there is no clear evidence for rejecting the
parallel lines assumption. The Sequential Sidak test starts with individual contrast Waldtests to
providean overall pvalue, andthese results should be comparable to the omnib us Waldtest result.
The fact that they are so different in this example is somewhat surprising but could be due to the
existence of many contrastsin the test and a relatively small design degrees of freedom.