Abstract
For square contingency tables with ordered categories, the present paper proposes an asymmetry model with m-additional parameters, which indicates (1) the generalized marginal homogeneity and (2) the structure of quasi-symmetry for cumulative probabilities. The proposed model includes a modified palindromic symmetry model by Iki, Oda and Tomizawa [7]. Also the present paper gives the decomposition of the symmetry model using the proposed model. Examples are given.
Highlights
IntroductionThe S model indicates that the probability that a father’s status is i and his son’s status is j, is equal to the probability that the father’s status is j and his son’s status is i
Consider the square contingency tables with same row and column classifications
The AS(1) model is identical to the modified palindromic symmetry (MPS) model
Summary
The S model indicates that the probability that a father’s status is i and his son’s status is j, is equal to the probability that the father’s status is j and his son’s status is i This model describes a structure of symmetry of the probabilities {pi j} with respect to the main diagonal of the table. The θis; jt (= (pi j/ps j)/(pit/pst)) indicates that the ratio of the odds that the father’s status is i instead of s when the son’s status is j to the odds that the father’s status is i instead of s when the son’s status is t. Tahata and Tomizawa [11] considered the m-additional parameters palindromic symmetry (PS(m)) model.
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