Abstract
For the analysis of square contingency tables with the same row and column ordinal classications, this article proposes a new model which indicates that the log-ratios of symmetric cell probabilities are proportional to the difference between log-row category and log-column category. The proposed model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate log-normal distribution. Also, this article gives the decomposition of the symmetry model using the proposed model with the orthogonality of test statistics. Examples are given. The simulation studies based on bivariate log-normal distribution are given.
Highlights
Consider an R × R square contingency table with the same row and column classifications
The f (u, v)/f (v, u) has the form ∆v−u, and the linear diagonals-parameter symmetry (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
We propose a model defined by pij = αlog iβlog jψij (i = 1, . . . , R; j = 1, . . . , R), where ψij = ψji
Summary
Consider an R × R square contingency table with the same row and column classifications. Agresti (1983) proposed the linear diagonals-parameter symmetry (LDPS) model, defined by pij = αiβjψij Agresti (1983) described the relationship between the LDPS model and the bivariate normal distribution with equal marginal variances as follows. The f (u, v)/f (v, u) has the form ∆v−u, and 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. We are interested in proposing a new model, which would be appropriate if it is reasonable to assume an underlying bivariate log-normal distribution.
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