Journal ArticleDOI
Power-divergence-type measure of departure from symmetry for square contingency tables that have nominal categories
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TLDR
In this article, the authors proposed a generalization of Tomizawa's measures by using the average of the power divergence of Cressie and Read, or the averaging of the diversity index of Patil and Taillie.Abstract:
For square contingency tables that have nominal categories, Tomizawa considered two kinds of measure to represent the degree of departure from symmetry. This paper proposes a generalization of those measures. The proposed measure is expressed by using the average of the power divergence of Cressie and Read, or the average of the diversity index of Patil and Taillie. Special cases of the proposed measure include Tomizawa's measures. The proposed measure would be useful for comparing the degree of departure from symmetry in several tables.read more
Citations
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The analysis of symmetry and asymmetry : orthogonality of decomposition of symmetry into quasi-symmetry and marginal symmetry for multi-way tables
Sadao Tomizawa,Kouji Tahata +1 more
TL;DR: In this article, the authors propose le modele de quasi-symetrie and montre qu'un tableau est symetrique si and seulement s'il satisfait a la fois quasi symetria and egalite des distributions marginales.
Journal ArticleDOI
Theory & Methods: Measure of Asymmetry for Square Contingency Tables Having Ordered Categories
TL;DR: In this paper, a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories) was proposed, expressed using the Cressie-Read power-divergence or Patil-Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j(> i) or above.
Journal ArticleDOI
Measure of departure from marginal homogeneity for square contingency tables having ordered categories
TL;DR: In this article, the authors proposed a measure to represent the degree of departure from marginal homogeneity for square contingency tables with ordered categories, which is expressed by using the Cressie and Read's (1984) power-divergence or Patil and Tail-lie's (1982) diversity index, defined for the cumulative probablities that an observation will fall in row (column) category i or below and column (row) categoryi + 1 or above.
Journal ArticleDOI
Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories
Kouji Tahata,Sadao Tomizawa +1 more
TL;DR: A generalized MH model is proposed, which describes a structure of the odds that an observation will fall in row category i or below and column category i + 1 or above, instead of in column categoryi orbelow and row category m-order moment of row and column variables.
Journal ArticleDOI
Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives
TL;DR: In this article, Cressie and Read introduced a class of multinomial goodness-of-fit statistics Ra based on power divergence, and proposed a new approximation of the power of Ra called the approximation AE approximation.
References
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TL;DR: In this article, the authors present a unified approach to model testing, including the use of the power-divergence measure in visual perception, which is a measure of loss and a criterion for general Parameter Estimation.