SUT J. Math. 57 (2), 147-165, (December 2021) DOI: 10.55937/sut/1641859466
Mana Aizawa, Shuji Ando, Kouji Tahata, Sadao Tomizawa
KEYWORDS: asymmetry, clinical study, ordered category, generalized marginal symmetry, marginal homogeneity, relationships among models, 62H17
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.