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An Estimate of the Covariance between Variables which are not Jointly Observed

Published online by Cambridge University Press:  01 January 2025

Robert Cudeck
Robert Cudeck*
Affiliation:
University of Minnesota
*
Requests for reprints should be sent to Robert Cudeck, Department of Psychology, University of Minnesota, 75 East River Road, Minneapolis MN 55455. E-Mail: [email protected]
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Abstract

Situations sometimes arise in which variables collected in a study are not jointly observed. This typically occurs because of study design. An example is an equating study where distinct groups of subjects are administered different sections of a test. In the normal maximum likelihood function to estimate the covariance matrix among all variables, elements corresponding to those that are not jointly observed are unidentified. If a factor analysis model holds for the variables, however, then all sections of the matrix can be accurately estimated, using the fact that the covariances are a function of the factor loadings. Standard errors of the estimated covariances can be obtained by the delta method. In addition to estimating the covariance matrix in this design, the method can be applied to other problems such as regression factor analysis. Two examples are presented to illustrate the method.

Keywords

missing datacovariance matrix estimationfactor analysis
Type
Notes And Comments
Information
Psychometrika , Volume 65 , Issue 4 , December 2000 , pp. 539 - 546
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

This research was partially supported by NIMH grant MH5-4576

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