Models and methods for the analysis of correlation coefficients

Abstract

The normal distribution plays a very prominant role in statistics, and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations. In this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways. For continuous multivariate analysis most of the existing large- sample theory can be applied without assuming multivariate normality. We also develop several discrete multinormal models. The first one is the classical Pearson model, which results from discreticizing multinormal variables. The second one is inspired by correspondence analysis, and the third one by loglinear analysis. The models are presented in terms of correlation coefficients, and applied to the Spearman model of factor analyses using an example from political science.