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Improper Solutions in the Analysis of Covariance Structures: Their Interpretability and a Comparison of Alternate Respecifications

Published online by Cambridge University Press:  01 January 2025

David W. Gerbing  and
James C. Anderson
David W. Gerbing*
Affiliation:
Baylor University
James C. Anderson
Affiliation:
J. L. Kellogg Graduate School of Management, Northwestern University
*
Requests for reprints should be sent to David W. Gerbing, Department of Psychology, Baylor University, Waco, TX 76798.
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Abstract

A Monte Carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis. Four models were studied with two sample sizes. Of the overall goodness-of-fit indices provided by the LISREL VI program significant differences between improper and proper solutions were found only for the root mean square residual. As expected, indicators of the factor on which the negative uniqueness estimate occurred had biased loadings, and the correlations of its factor with other factors were also biased. In contrast, the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance. For initial solutions with one negative uniqueness estimate, three respecifications were studied: Fix the uniqueness at .00, fix it at .20, or constrain the domain of the solution to be proper. For alternate, respecified solutions that were converged and proper, the constrained solutions and uniqueness fixed at .00 solutions were equivalent. The mean goodness-of-fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at .00 respecifications.

Keywords

improper solutionsanalyses of covariance structuresconfirmatory factor analysismaximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 1 , March 1987 , pp. 99 - 111
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

This investigation was supported in part by a grant from the Baylor University Research Committee (#018-F83-URC). The authors gratefully acknowledge the comments and suggestions of Claes Fornell and Roger E. Kirk, and the assistance of Timothy J. Vance with the analysis.

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