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Comparing Regressions when Measurement Error Variances are known

Published online by Cambridge University Press:  01 January 2025

T. W. F. Stroud
T. W. F. Stroud*
Affiliation:
Queen's University Educational Testing Service
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Abstract

In a multiple (or multivariate) regression model where the predictors are subject to errors of measurement with a known variance-covariance structure, two-sample hypotheses are formulated for (i) equality of regressions on true scores and (ii) equality of residual variances (or covariance matrices) after regression on true scores. The hypotheses are tested using a large-sample procedure based on maximum likelihood estimators. Formulas for the test statistic are presented; these may be avoided in practice by using a general purpose computer program. The procedure has been applied to a comparison of learning in high schools using achievement test data.

Keywords

CovarianceRegression ModelPublic PolicyStatistical TheoryError Variance
Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 1 , March 1974 , pp. 53 - 68
Copyright
Copyright © 1974 The Psychometric Society

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Footnotes

*

The main results in this paper were first obtained as part of the author's Ph.D. dissertation at Stanford University, under the supervision of Professor Ingram Olkin and with the partial support of National Science Foundation grants GP-6681 and GP-27210. The author wishes to thank the Portland School District Administration for the use of their data. The author is grateful for the comments of Dr. Frederic M. Lord.

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