A1407
Title: Interpretation of marginal homogeneity based on decomposition and visualization in collapsed ordinal tables
Authors: Satoru Shinoda - Yokohama City University (Japan) [presenting]
Kouji Yamamoto - Yokohama City University (Japan)
Sadao Tomizawa - Tokyo University of Science (Japan)
Abstract: Marginal homogeneity (MH) is a fundamental concept for analyzing paired ordinal data in square contingency tables. When ordinal categories are collapsed to simplify interpretation, multiple collapsing patterns arise, making it difficult to assess MH within a unified framework. A framework for interpreting MH based on marginal cumulative distributions is introduced. First, a new model, termed collapsed marginal mean equality (CoME) for collapsed tables is proposed. Together with extended marginal homogeneity (EMH), it is shown that the MH model holds if and only if both the CoME and EMH models hold. Second, to enable comparisons across tables, a Kullback Leibler information type measure of departure from MH that incorporates ordinal structure is introduced. It is further shown that this measure can be decomposed into components corresponding to CoME and EMH, allowing identification of whether deviations arise from proportional scaling or differences in distributional shape. Finally, to facilitate intuitive interpretation, a visualization approach that displays the CoME and EMH sub-measures for each collapsing pattern is presented. Real data examples demonstrate the practical utility of the proposed framework.
