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Analysis of Covariance Structures

Published online by Cambridge University Press:  01 January 2025

R. Darrell Bock  and
Rolf E. Bargmann
R. Darrell Bock
Affiliation:
University of North Carolina
Rolf E. Bargmann
Affiliation:
I. B. M. Corporation
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Abstract

A general method is presented for estimating variance components when the experimental design has one random way of classification and a possibly unbalanced fixed classification. The procedure operates on a sample covariance matrix in which the fixed classes play the role of variables and the random classes correspond to observations. Cases are considered which assume (i) homogeneous and (ii) nonhomogeneous error variance, and (iii) arbitrary scale factors in the measurements and homogeneous error variance. The results include maximum-likelihood estimations of the variance components and scale factors, likelihood-ratio tests of the goodness-of-fit of the model assumed for the design, and large-sample variances and covariances of the estimates. Applications to mental test data are presented. In these applications the subjects constitute the random dimension of the design, and a classification of the mental tests according to objective features of format or content constitute the fixed dimensions.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 4 , December 1966 , pp. 507 - 534
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

Preparation of this paper has been supported in part by NSF Grant GB-939 and U. S. P. H. Grant GM-1286-01. Computer time was donated by the Computation Center, University of Chicago.

†

Now at the University of Chicago.

‡

Now at the University of Georgia.

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