An index to simultaneously analyze the degree and directionality of departure from global marginal homogeneity in square contingency tables

2021 ◽  
Author(s):  
Shuji Ando
Keyword(s):  
Contingency Tables ◽  
Marginal Homogeneity

A Decomposition of the Marginal Homogeneity Model for Square Contingency Tables with Ordered Categories

1993 ◽  
Vol 43 (1-2) ◽  
pp. 123-126 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Short Note ◽  
Monotonic Function ◽  
Ordered Categories ◽  
Marginal Homogeneity ◽  
Statist Assoc

For square contingency tables, with ordered categories, this short note decomposes the marginal homogeneity (MH) model into an extended MH model and the model of equality of expectation of monotonic function of row and column variables. This decomposition is a generalization of the decomposition of the MH model which was earlier considered by Tomizawa (1991, Cal. Statist. Assoc. Bull., 41, 201-207).

scholarly journals Two-Dimensional Measure Vector of Departure from Marginal Homogeneity in Square Contingency Tables

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Shuji Ando ◽  
◽  
Takashi Takeuchi ◽  
Kiyotaka Iki ◽  
Sadao Tomizawa ◽  
...  
Keyword(s):  
Contingency Tables ◽  
Two Dimensional ◽  
Marginal Homogeneity ◽  
Dimensional Measure

Decomposition of Bivariate Symmetric Density Function

1996 ◽  
Vol 46 (1-2) ◽  
pp. 129-134
Author(s):  
Takashi Sadao Tomizawa Seo ◽  
Jun-Ichiro Minaguchi
Keyword(s):  
Density Function ◽  
Contingency Tables ◽  
Marginal Homogeneity ◽  
Symmetric Density ◽  
Symmetry Model ◽  
Bivariate Density

For the analysis of square contingency tables, it is known that the symmetry model holds if and only if both the quasi-symmetry and the marginal homogeneity models hold (Caussinus, 1965; Bishop et al., 1975, p. 287). This paper shows that a similar decomposition for bivariate density function (instead of cell probabilities) holds.

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

2018 ◽  
Vol 7 (4) ◽  
pp. 27 ◽  
Author(s):  
Yusuke Saigusa ◽  
Tomohisa Maruyama ◽  
Kouji Tahata ◽  
Sadao Tomizawa
Keyword(s):  
Data Analysis ◽  
Logistic Model ◽  
Contingency Tables ◽  
Occupational Status ◽  
Marginal Homogeneity ◽  
The Poor ◽  
Proposed Model ◽  
Marginal Means ◽  
Status Data ◽  
Square Tables

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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