Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, this paper proposes a model which indicates the structure of marginal asymmetry. The model states that the absolute values of logarithm of ratio of the cumulative probability that an observation will fall in row category i or below and column category i + 1 or above to the corresponding cumulative probability that the observation falls in column category i or below and row category i + 1 or above are constant for every i. We deal with the estimation problem for the model parameter and goodness-of-fit tests. Also we discuss the relationships between the model and a measure which represents the degree of departure from marginal homogeneity. Examples are given.

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“…Tahata and Tomizawa [13] proposed the m-additional parameters MH (MH(m)) model defined by; for a given m (m = 1, . .…”

Section: Discussionmentioning

confidence: 99%

“…These data have been analyzed by many statisticians, for example, Stuart [11], Bartolucci and Scaccia [2], Tahata and Tomizawa [13] and Ng et al [9].…”

Section: Examplementioning

confidence: 99%

Marginal asymmetry model for square contingency tables with ordered categories

Tahata

Yoshimoto

2014

Journal of Applied Statistics

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“…We refer to such relation as a decomposition of model (i.e., the MH model is decomposed into the ML model and the equality of row and column marginal means). Also, see Tahata & Tomizawa (2008) and Kurakami, Tahata & Tomizawa (2013) for the decompositions of the MH model. We are interested in whether the decomposition with the ML model replaced by the proposed model holds or not.…”

Section: Introductionmentioning

confidence: 99%

Extended Marginal Homogeneity Model Based on Complementary Log-Log Transform for Square Tables

Saigusa¹,

Maruyama²,

Tahata³

et al. 2018

IJSP

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For square contingency tables with the same ordinal row and column classifications, McCullagh (1977) gave the marginal cumulative logistic model, which is an extension of the marginal homogeneity (MH) model using the logit transform. The present paper proposes a different extension of the MH model using the complementary log-log transform. In addition, the present paper gives the theorem that the MH model is equivalent to the proposed model and the equality of row and column marginal means holding simultaneously. In data analysis, if the MH model fits the data poorly, the theorem may be useful for seeing the reason for the poor fit. As example, the occupational status data for British father-son pairs are analyzed.

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“…Tahata and Tomizawa [13] considered the m-additional parameters marginal homogeneity (MH(m)) model which is a generalization of the MH model. For a given m (m = 1, .…”

Section: Introductionmentioning

confidence: 99%

A generalized asymmetry model for square contingency tables with ordered categories

Iki

Suto²,

Tomizawa

2016

JSTA

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For square contingency tables with ordered categories, the present paper proposes an asymmetry model with m-additional parameters, which indicates (1) the generalized marginal homogeneity and (2) the structure of quasi-symmetry for cumulative probabilities. The proposed model includes a modified palindromic symmetry model by Iki, Oda and Tomizawa [7]. Also the present paper gives the decomposition of the symmetry model using the proposed model. Examples are given.

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Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories

Abstract: Generalized marginal homogeneity, Kurtosis, Marginal homogeneity, Moment, Ordered category, Skewness, Square contingency table, 62H17, C39,

Cited by 20 publications

References 14 publications

Marginal asymmetry model for square contingency tables with ordered categories

Marginal asymmetry model for square contingency tables with ordered categories

Extended Marginal Homogeneity Model Based on Complementary Log-Log Transform for Square Tables

A generalized asymmetry model for square contingency tables with ordered categories

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