Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications

David W. Gerbing*, James C. Anderson

*Corresponding author for this work

Research output: Contribution to journalArticle

100 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)99-111
Number of pages13
JournalPsychometrika
Volume52
Issue number1
DOIs
StatePublished - Mar 1 1987

Keywords

  • analyses of covariance structures
  • confirmatory factor analysis
  • improper solutions
  • maximum likelihood

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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