Geometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered Categories

Tomoyuki Nakagawa,Aki Ishii,Sadao Tomizawa,Toshiki Takei

doi:10.3844/jmssp.2020.170.175

Tomoyuki Nakagawa, Aki Ishii + Show 2 more

Open Access

https://doi.org/10.3844/jmssp.2020.170.175

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Abstract

For square contingency tables, some studies have developed the weighted arithmetic mean type measure to represent the degree of departure from the marginal homogeneity. The present paper proposes (1) the cumulative partial marginal homogeneity model which has the weaker restriction than the marginal homogeneity model and (2) the measure to represent the degree of departure from the proposed model. The measure is expressed as a weighted geometric mean of the diversity index. Finally, numerical studies are presented.

Highlights

Consider an r × r square contingency table with the same row and column classifications
The Partial Marginal Homogeneity (PMH) model indicates that the row marginal distribution is identical to the column marginal distribution for at least one i
The measure to represent the degree of departure from the Cumulative Partial Marginal Homogeneity (CPMH) model is proposed as follows:

Summary

Introduction

Consider an r × r square contingency table with the same row and column classifications. Tomizawa (2001) gave the measure to represent the degree of departure from the MH model for square contingency tables with nominal categories. We propose a new model which has the structure of the cumulative partial marginal homogeneity for an r × r contingency table with ordered categories. We propose the geometric mean type measure to represent the degree of departure from the new model. The measure to represent the degree of departure from the CPMH model is proposed as follows: G1* i G2* i.

5: Values of

Concluding Remarks