The Structure of the Log Odds-Ratios in Non-Independence and Symmetry Diagonal Models for Square Contingency Tables

Abstract

This paper examines the structure of the interaction term when expressed as the log ofthe odds-ratios ij in the log-linear model formulation of non-independence and symmetry diagonalmodels applied to an I x I contingency table having ordinal classificatory variables. The class ofprincipal diagonal, diagonal band, full diagonal and diagonal-parameters symmetry models areexamined in the study. The general structure of Φij is examined for each class of diagonal models.The 5 x 5 British Social Mobility data (Glass, 1954) will be employed as an example in this paper.The structure of the log odds-ratios are formulated in terms of the parameter estimates obtained from the application of SAS PROC GENMOD. Goodman in several of his papers on the subject has also derived some of these log odds ratios but our focus here is the structure of these odds, when viewed from the non-standard log-linear perspective (Lawal, 2001, 2002).