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Testing Pattern Hypotheses for Correlation Matrices

Published online by Cambridge University Press:  01 January 2025

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

McDonald [1974] obtained Maximum Likelihood (ML) estimates of the free parameters, and an asymptotic likelihood-ratio test, for the hypothesis that one or more elements of a covariance matrix are zero, and/or that groups of two or more of its elements are equal. Estimation was by Newton's method, starting from a closed-form Least Squares (LS) solution that is typically close to the ML solution point. The hypothesis can also be tested using the general model for the analysis of covariance structures given by Jöreskog [1970], but the combination of a closed-form LS starting point and the classical Newton method given by McDonald yields estimates in about a quarter of the computer time needed by JOreskog's program, ACØVS.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 253 - 255
Copyright
Copyright © 1975 The Psychometric Society

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References

Jöreskog, K. G. A general method for analysis of covariance structures. Biometrika, 1970, 239–251.CrossRefGoogle Scholar
McDonald, R. P.. Testing pattern hypotheses for covariance matrices. Psychometrika, 1974, 39, 189–201.CrossRefGoogle Scholar
McDonald, R. P., and Swaminathan, H.. A simple matrix calculus with applications to multivariate analysis. General Systems, 1973, 18, 37–54.Google Scholar