Title: Measures of ordinal association in two-way contingency tables
Authors: Maria Kateri - RWTH Aachen University (Germany) [presenting]
Abstract: For $IxJ$ contingency tables with ordinal classification variables, measures of association are discussed that are based on generalized odds ratios (GORs). The GORs are linked to association models and expressed in terms of their parameters. Since the maximum likelihood estimation of the association models' parameters requires the use of iterative procedures, closed-form approximations to the maximum likelihood estimators (MLEs) are considered that allow for a handy estimation of the corresponding association measures. In the literature there exist some measures of this type that are related to the uniform association ($U$) model. We introduce new measures, based on the row effect association ($R$) model, that are more flexible in capturing structures of underlying association other than the uniform. Furthermore, we propose alternative closed-form estimators for measures based on $U$ and $R$ models. The new measures are illustrated via examples while the various closed-form approximations are compared to the MLEs via extensive simulation studies.