Linear Diagonals-parameter Symmetry Model Research Articles

An Extended Bivariate T-Distribution Type Symmetry Model for Square Contingency Tables

The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.

Decomposition of Symmetry into Ordinal Quasi-Symmetry and Marginal Equimoment for Multi-way Tables

For the analysis of square contingency tables with ordered categories, Agresti (1983) introduced the linear diagonals-parameter symmetry (LDPS) model. Tomizawa (1991) considered an extended LDPS (ELDPS) model, which has one more parameter than the LDPS model. These models are special cases of Caussinus (1965) quasi-symmetry (QS) model. Caussinus showed that the symmetry (S) model is equivalent to the QS model and the marginal homogeneity (MH) model holding simultaneously. For square tables with ordered categories, Agresti (2002, p.430) gave a decomposition for the S model into the ordinal quasi-symmetry and MH models. This paper proposes some decompositions which are different from Caussinus’ and Agresti’s decompositions. It gives (i) two kinds of decomposition theorems of the S model for two-way tables, (ii) extended models corresponding to the LDPS and ELDPS, and the generalized model further for multi-way tables, and (iii) three kinds of decomposition theorems of the S model into their models and marginal equimoment models for multi-way tables. The proposed decompositions may be useful if it is reasonable to assume the underlying multivariate normal distribution.

Decomposition of Generalized Asymmetry Model for Square Contingency Tables

For the analysis of square contingency tables with same row and column ordinal classifications, the present paper gives the decomposition of the generalized linear diagonals-parameter symmetry model using the diagonals-parameter symmetry model. Moreover, it gives the decomposition of the symmetry model using above the proposed decomposition.

Decompositions of Symmetry Using Generalized Linear Diagonals-Parameter Symmetry Model and Orthogonality of Test Statistic for Square Contingency Tables

For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.

Generalized Linear Asymmetry Model and Decomposition of Symmetry for Multiway Contingency Tables

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

A measure of linear diagonals-parameter symmetry for square contingency tables with ordered categories

For square contingency tables with ordered categories, Agresti (1) considered the linear diagonals-parameter symmetry (LDPS) model being an extension of the symmetry model. This paper proposes a measure which represents the degree of departure from the LDPS model. The measure proposed is expressed using the Cressie-Read power-divergence or Patil-Taillie diversity index. The measure is useful for comparing the degree of departure from LDPS in several tables, and it may be appropriate for comparing the degrees of departure from the equality of the marginal variances for several square ordinal tables if it is reasonable to assume underlying bivariate normal distributions. Examples are also given.

Diagonal, weighted marginal homogeneity model and decompositions for linear diagonals-parameter symmetry model

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