3 articles for “Marginal Homogeneity”

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Research ArticleOpen accessPhrase in the titleGeometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered CategoriesTomoyuki Nakagawa, Toshiki Takei, Aki Ishii, Sadao TomizawaFor 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 … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 11 Aug 2020 · 6,625 accessesView PDF Cite

Research ArticleOpen accessPhrase in the titleDecomposition of Marginal Homogeneity into Logit and Mean Ridits Equality for Square Contingency TablesKiyotaka Iki, Kouji Tahata, Sadao TomizawaProblem statement: For square contingency tables with ordered categories, if the Marginal Homogeneity (MH) model holds, then the probability that X selected at random from the row marginal distribution is less than Y selected independently at random from the column marginal distribution equals the probability that X is greater than Y. However, the converse does not hold. We are interested … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,302 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsDecompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered CategoriesKouji Yamamoto, Satoru Shinoda, Sadao TomizawaProblem statement: For square contingency tables with ordered categories, this study considers four kinds of extensions of the marginal homogeneity model and gives decompositions for the ordinal quasi-symmetry model. The decompositions are extensions of some existing decompositions. Approach: This study gives a decomposition theorem that the ordinal quasi-symmetry model holds if and only if the quasi-symmetry model and the proposed … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 28 Oct 2011 · 7,154 accessesView PDF Cite