Contaminated Normal Type Symmetry Model and Decomposition of Symmetry for Square Contingency Tables

Abstract

For the analysis of square contingency tables with ordered categories, Agresti (1983) considered the linear diagonals-parameter symmetry (LDPS) model being an extension of the symmetry (S) model, which may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate normal distribution with equal marginal variances. This paper proposes another extension of the S model which may be appropriate for a square ordinal table if it is reasonable to assume an underlying e-contaminated bivariate normal distribution with equal marginal variances included in the class of elliptical distributions. The proposed model has a structure of weighted mixture of two LDPS models. Moreover, this paper gives a theorem that the S model holds if and only if both the proposed model and the marginal means equality model hold. The simulation studies based on the e-contaminated bivariate normal distribution are given.