Orthogonal decomposition of point-symmetry for multiway tables

Abstract

Likelihood ratio statistic, Marginal point-symmetry, Quasi point-symmetry, Separability, Square contingency table,

On Decomposition of Point-Symmetry for Square Contingency Tables With Ordered Categories

“…In the similar way to Theorem 1, the following theorem can be obtained: (also see Tomizawa [9]; Tahata and Tomizawa [8]). Tomizawa [10] The CPS model indicates that…”

“…Tomizawa and Tahata [8] proposed the quasi point-symmetry model and the marginal point-symmetry model, and considered the decomposition of the PS model using these models. We are now interested in considering the decompositions of the PS model in the similar manner to Theorems 1 and 2.…”

Generalized Exponential Symmetry Model and Orthogonal Decomposition of Symmetry for Square Tables

“…Aitchison [12] discussed the asymptotic separability, which is equivalent to the orthogonality in Read [6] and the independence in Darroch and Silvey [13], of test statistic for the goodness-of-fit of two models (also see Lang and Agresti [10]; Lang [11]; Tomizawa and Tahata [7]; Tahata and Tomizawa [14]). …”

Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

“…Some examples for these kind of tables are: for instance, when the subjects are measured at two di erent points in time (e.g., responses before and after experiments); the decisions of two experts are measured on the same set of subjects (e.g., the grading of the same cancer tumors by two specialists); two similar units in a sample are measured (e.g., the grades of vision of the left and the right eyes); matched pair experiments (e.g., social status of the fathers and sons) [1]. For square contingency tables, several models have been proposed (see, for example [2][3][4][5][6][7][8] but the models of symmetry (S), quasi-symmetry (QS), marginal homogeneity (MH) are classical and well known models [9,10] and the applicability of the these models is straightforward. The QS is less restrictive model than the S model [11][12][13].…”