Odds ?symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables

This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for alli<j, that an observation will fall in row categoryi or below, and column categoryj or above, instead of row categoryj or above, and column categoryi or below, depend on only row categoryi or column categoryj. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse is not necessarily true. This study also shows that it is necessary to satisfy the extended marginal homogeneity model, in addition to the proposed models, to satisfy the CS model. These decomposition theorems explain why the CS model does not hold. The proposed models provide a better fit for application to a single data set of real-world occupational data for father-and-son dyads.

Source: Australian and New Zealand Journal of Statistics - January 11, 2022 Category: Statistics Authors: Shuji Ando Tags: Original Article Source Type: research