Normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories

For square contingency tables with ordered categories, this paper proposes a model that the cell probabilities have a similar structure of bivariate normal density function with equal marginal variances. The proposed model is special cases of Agresti's linear diagonals-parameter symmetry model and Goodman's diamond model. Examples with real data are given and the simulation studies based on the bivariate normal distribution are also given.