Association models and the bivariate normal for contingency tables with ordered categories

Association models considered by Goodman (1979) for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal. Association models can be applied when an underlying bivariate normal is assumed and also under more general conditions, and they provide alternatives to tetrachoric and polychoric correlation. These models agree more closely with the bivariate normal than does Plackett's model (1965), when the row and column classifications arise from underlying univariate normal distributions. The general utility of the association models is illustrated here.