Model based on skew normal distribution for square contingency tables with ordinal categories

For the analysis of square contingency tables with ordinal categories, Tahata, Yamamoto and Tomizawa (2009) considered the normal distribution type symmetry model, which may be appropriate if it is reasonable to assume an underlying bivariate normal distribution with equal marginal variances. The present paper proposes a new model which may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate skew normal distribution with equal marginal variances. Simulations are used to investigate the fitting of new model for bivariate skew normal distribution. The decayed teeth data are analyzed by using the new model.