For the analysis of square contingency tables with ordered categories, Agresti (1983) introduced linear diagonals-parameter symmetry (LDPS) model. Tomizawa (1991) considered an extended LDPS (ELDPS) model, which has one more parameter than These models are special cases Caussinus (1965) quasi-symmetry (QS) showed that (S) model is equivalent to QS and marginal homogeneity (MH) holding simultaneously. (2002, p.430) gave a decomposition for S into ordinal MH models. This paper proposes some...

For analyzing square contingency tables, Bowker [14] proposed the symmetry model. Caussinus [16] quasi-symmetry model and gave a decomposition of such that holds if only both marginal homogeneity models hold. Bhapkar Darroch [13] similar theorem for multi-way tables. tables present paper (1) reviews various asymmetry, (2) decompositions models, (3) gives some figures which indicate relationships among (4) new

For square contingency tables that have nominal categories, Tomizawa considered two kinds of measure to represent the degree departure from symmetry. This paper proposes a generalization those measures. The proposed is expressed by using average power divergence Cressie and Read, or diversity index Patil Taillie. Special cases include Tomizawa's would be useful for comparing symmetry in several tables.

For the analysis of square contingency tables with ordered categories, Goodman (1979, Biometrika 66, 413-418) considered diagonals-parameter symmetry (DPS) model, which has a multiplicative form for cell probabilities. This paper proposes another DPS model similar cumulative probabilities that an observation will fall in row (column) category i or below and column (row) j (>i) above. Special cases proposed include conditional symmetry. The relationship stochastic ordering marginal...

For the analysis of square contingency tables with ordered categories, three kinds decompositions for conditional symmetry model derived by Tomizawa are simply described. Using and its decomposed models, this paper analyzes data unaided distance vision women in Britain first analyzed Stuart, students a university Japan, pupils at elementary schools city Tokyo.

For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent degree departure from symmetry. This paper proposes a measure represents asymmetry for ordered categories (instead those categories). The proposed is expressed using Cressie–Read power‐divergence or Patil–Taillie diversity index, defined cumulative probabilities an observation falls in row (column) category i below column (row) j (> ) above. depends on...

Abstract For square contingency tables with ordered categories, Agresti (1983) considered the linear diagonals‐parameter symmetry model. An extended model including that is proposed which has only one more parameter than The also includes conditional by McCullagh (1978). Decompositions for and Agresti's are given.

Yamamoto, Iwashita, and Tomizawa (2007) gave the decompositions of symmetry (S) model into extended S two or three marginal equimoment models for multi-way tables with ordered categories. However goodness-of-fit test statistic is not asymptotically equivalent to sum those decomposed four models. This paper gives, tables, modification their such that one modified model, which constraints combined means equality variances equality, correlations equality. Examples are given.

Abstract The decomposition for the complete point symmetry model in a rectangular contingency table is shown. Also respective decompositions local and reverse square are given. Moreover test procedures decomposed models an example

Abstract For the analysis of square contingency tables with ordered categories, Caussinus (1965) considered quasi‐symmetry (QS) model, Goodman (1979) diagonals‐parameter symmetry (DPS) and Agresti (1983) linear (LDPS) model. These models show structures for cell probabilities. Tomizawa (1993) proposed another DPS model which has a similar multiplicative form cumulative probabilities that an observation will fall in row (column) category i or below column (row) j (> ) above. This paper...

A k-order generalization of the linear diagonals-parameter symmetry model is proposed, and related orthogonal decompositions are inspected.Applications to randomized clinical trials given.

For square contingency tables with ordered categories, Agresti (1984, 2002) considered the marginal cumulative logistic (ML) model, which is an extension of homogeneity (MH) model. The ML model depends on probabilities main diagonal table. This paper (1) proposes conditional (CML) does not depend diagonal, and (2) decomposes MH into indicates equality row column means. Examples are given.

Abstract For the analysis of square contingency tables with ordinal classifications, marginal homogeneity (MH) model is one important models. Some measures for analyzing degree departure from MH have been proposed. This study proposes a new measure using continuation odds. Continuation odds may be considered as discrete time hazard. The proposed expressed in form Cressie-Read’s power-divergence (including Kullback-Leibler divergence) or Patil and Taillie’s diversity index Shannon entropy)....

For square contingency tables with nominal categories, four kinds of measure are proposed to represent the degree departure from marginal homogeneity (MH). The measures expressed by using Shannon entropy or Gini concentration. They used how far distributions (or conditional given that an observation will fall in one off-diagonal cells table) distant those MH structure. Two these also extended T-way (T ≥ 3).

For square contingency tables rith ordered categories, this paper proposes two kinds of extensions marginal homogeneity model and gives decompositions for the Liseer diagonals-parameter symmetry considered by Agresti (1983a) using proposed models- The models are also applied to an unaided vision data.

For square contingency tables, the present paper newly considers partial symmetry model which indicates that there is a symmetric structure of probabilities for at least one pairs cells. It also proposes measure to express degree departure from model. Examples are given.

Abstract For the analysis of square contingency tables with same row and column ordinal classifications, this study proposes an index for measuring degree departure from symmetry model using new cumulative probabilities. The proposed is constructed based on Cressie Read’s power divergence, or weighted average Patil Taillie’s diversity index. This derives a plug-in estimator approximate confidence interval expected to reduce bias more than existing index, even when sample size not large....

For the analysis of square contingency tables with ordered categories, this paper introduces quasi­diagonals­parameter symmetry (QDPS) model which is an extension quasi­symmetry (QS) model. It shown that QDPS preferable to QS for unaided vision data British women earlier analysed by Stuart (1955). Various extended models are expressed in terms local odds ratios and other ratios.

For square contingency tables with ordered categories, this paper proposes a measure to represent the degree of departure from marginal homogeneity model. It is expressed as weighted sum power-divergence or Patil–Taillie diversity index, and function log odds ratios. The represents equality that row variable i below instead i+1 above column for every i. also extended multi-way tables. Examples are given.

For the analysis of square contingency tables, many kinds symmetry models have proposed. The present paper proposes a new kind model, and gives decomposition model by introducing an extended it. Moreover, it shows orthogonality statistic for testing goodness-of-fit model. Two unaided vision data analyses are also shown.