Non-inferiority marginal symmetry model and its decomposition for ordinal square contingency tables

Abstract

The marginal homogeneity (MH) model is well-known for analyzing ordinal square contingency tables. This study proposes a non-inferiority marginal symmetry (NiMS) model, which has a different marginal symmetry structure than the MH model. In the NiMS model, the probability of an observation falling in row category $i$ or below and column category $i$ or above is equal to the probability of an observation falling in row category $i$ or above and column category $i$ or below. Additionally, two kinds of extended NiMS models are proposed. These extended NiMS models constantly hold when the NiMS model holds. However, the converse is not necessarily true. This study examines what a model should be necessary, in addition to the extended NiMS model, to satisfy the NiMS model.