Discrete Normal Linear Regression Models

In this paper we continue our study of the Pearsonian approach to discrete multivariate analysis, in which structural properties of the multivariate normal distribution are combined with the essential discreteness of the data into a single comprehensive model. In an earlier publication we studied these ‘block-multinormal’ methods for covariance models. Here we propose a similar approach for the regression model with fixed regressors. Likelihood methods are derived and applied to some examples. We review the related literature and point out some interesting possible generalizations. The effect of continuous misspecification of a discrete model is studied in some detail. Relationships with the optimal scaling approach to multivariate analysis are also investigated.