Analysis of covariance and correlation structures

A new estimation method, the two-stage constrained maximum likelihood procedure, is developed and it is shown that either the sample covariance or the correlation matrix can be used in analyzing the correlation structure.

Abstract

The main purpose of this paper is to consider different approaches in analyzing covariance or correlation structures with parameters subject to general nonlinear constraints. A new estimation method, the two-stage constrained maximum likelihood procedure, is developed. While in large samples this procedure is shown to have similar statistical properties to the classical constrained maximum likelihood approach, computationally it requires less computer time and storage to implement. It is shown that either the sample covariance or the correlation matrix can be used in analyzing the correlation structure. Examples are given to illustrate the theory, and technical details are presented in the Appendix.