Odds Ratios
Cumulative odds are defined as the ratio of the probability that the dependent variable takes a value less than or equal to a given response category to the probability that it takes a value greater than that response category. The cumulative odds ratio is the ratio of cumulative odds for different predictor values and is closely related to the exponentiated parameter estimates. Interestingly, the cumulative odds ratio itself does not depend upon the response category.
This table displays cumulative odds ratios for the factor levels of Age category. The reported values are the ratios of the cumulative odds for 18–30 through 46–60, compared to the cumulative odds for >60. Thus, the odds ratio of 1.383 in the first row of the table means that the cumulative odds for a person aged 18–30 are 1.383 times the cumulative odds for a person older than 60. Note that because Age category is not involved in any interaction terms, the odds ratios are merely the ratios of the exponentiated parameter estimates. For example, the cumulative odds ratio for 18–30 vs. >60 is 1.00/0.723 = 1.383.
This table displays the cumulative odds ratios for the factor levels of Driving frequency, using 10–14,999 miles/year as the reference category. Since Driving frequency is not involved in any interaction terms, the odds ratios are 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.