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

Shuji Ando, Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, Katsushika-ku, Tokyo, Japan, Takashi Takeuchi, Kiyotaka Iki, Sadao Tomizawa, Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan, Department of Economics, Nihon University, Chiyoda-ku, Tokyo, Japan, Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan
2019 Journal of Advanced Statistics  

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For square contingency tables with ordered categories, Tahata et al. (2006) and Tahata et al. (2012) considered measures which represent the degree of departure from the marginal homogeneity (MH) model using the cumulative marginal probabilities. The former measure can judge whether or not the MH model holds, but the latter cannot. Also, the latter measure can distinguish the directionality for two types of maximum marginal inhomogeneities, but the former cannot. The present paper proposes a
more » ... -dimensional measure vector with above measures as elements that can simultaneously analyze the degree of departure from MH and the directionality for two types of maximum marginal inhomogeneities. Also, this paper shows the usefulness of the proposed measure vector on comparing visually degrees of departure from MH in several square contingency tables using confidence region.
doi:10.22606/jas.2019.43001 fatcat:qnuzam6msffcte6nko36tobtbq
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Shuji Ando, Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, Katsushika-ku, Tokyo, Japan, Takashi Takeuchi, Kiyotaka Iki, Sadao Tomizawa, Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan, Department of Economics, Nihon University, Chiyoda-ku, Tokyo, Japan, Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan. "Two-Dimensional Measure Vector of Departure from Marginal Homogeneity in Square Contingency Tables." Journal of Advanced Statistics 4.3 (2019)