Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories

Abstract A class of models is proposed for the analysis of association in a contingency table with ordered rows and ordered columns. Association is measured in terms of the odds-ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns. This class includes the null association model, the uniform association model, and models that describe the possible effects of the rows and/or columns on the association. With these models, the association in the table can be analyzed in a manner analogous to the usual two-way analysis of variance, and parsimonious descriptions of this association can be obtained often. Applications are discussed here, some well-known sets of data are reanalyzed, and new insights into these data are obtained.