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Testing Pattern Hypotheses for Covariance Matrices

Published online by Cambridge University Press:  01 January 2025

R. P. McDonald
R. P. McDonald*
Affiliation:
The Ontario Institute for Studies in Education
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Abstract

Maximum likelihood estimates of the free parameters, and an asymptotic likelihood-ratio test, are given for the hypothesis that one or more elements of a covariance matrix are zero, and/or that two or more of its elements are equal. The theory applies immediately to a transformation of the covariance matrix by a known nonsingular matrix. Estimation is by Newton's method, starting conveniently from a closed-form least-squares solution.

Numerical illustrations include a test for equality of diagonal blocks of a covariance matrix, and estimation of quasi-simplex structures.

Keywords

CovarianceCovariance MatrixPublic PolicyFree ParameterMaximum Likelihood Estimate
Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 2 , June 1974 , pp. 189 - 201
Copyright
Copyright © 1974 The Psychometric Society

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