Abstract
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.
Highlights
Consider an R × R square contingency table with the same row and column ordinal classifications
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
Summary
Consider an R × R square contingency table with the same row and column ordinal classifications. Tomizawa [4] proposed an extended linear diagonals-parameter symmetry (ELDPS) model defined by ( ) θ θ = p p j−i j2−i2 ij ji i< j This indicates that the probability that an observation will fall in the (i, j ) th cell, i < j , is θ θ j−i j2−i2 12 times higher than the probability that it falls in the ( j,i) th cell. Agresti [3] [5] described the relationship between the LDPS model and the joint bivariate normal distribution as follows: the LDPS model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate normal distribution with equal marginal variances. Tomizawa [4] pointed out that the ELDPS model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate normal distribution with different marginal variances.
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