Describing ordinal odds ratios for stratified r x c tables
by
Ivy Liu
Victoria University of Wellington

The odds ratio is a common measurement for comparing binary responses for two groups. When the response is ordinal, such as ``better'', ``unchanged'', or ``worse'', we consider an ordinal odds ratio having a global view on the response that utilizes cumulative probabilities of the response variable. When both response and group variable have natural ordering, different ordinal odds ratios that describe association between the explanatory and the response variables can be measured. For instance, a proportional odds model that ignores the ordering of the explanatory variable assumes that the ordinal odds ratio is ``global'' in the response and is ``local'' in the groups. Besides, several authors (Pearson and Heron, 1913; Plackett, 1965; and Dale, 1984) have discussed another ordinal odds ratio that is ``global'' in both the response and group variables. We refer to the former one as local-global odds ratio and the latter one as global odds ratio. For cases in which a stratification factor is involved, this talk will propose simple Mantel-Haenszel-type estimators to summarize the local-global odds ratio and the global odds ratio from several strata. Compared to the maximum likelihood estimator, simulations show that the proposed estimators have better performance especially when each stratum has few observations. Also, a study of hatching for baby skinks will be discussed.

Date received: August 27, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahg-30.