Improper Solutions in Structural Equation Models

Feinian Chen, Kenneth A. Bollen, Pamela Paxton, Patrick J. Curran and James B. Kirby
Additional contact information
Feinian Chen: University of North Carolina at Chapel Hill
Kenneth A. Bollen: University of North Carolina at Chapel Hill
Pamela Paxton: Ohio State University
Patrick J. Curran: University of North Carolina at Chapel Hill
James B. Kirby: Agency for Healthcare Research and Quality

Sociological Methods & Research, 2001, vol. 29, issue 4, 468-508

Abstract: In this article, the authors examine the most common type of improper solutions: zero or negative error variances. They address the causes of, consequences of, and strategies to handle these issues. Several hypotheses are evaluated using Monte Carlo simulation models, including two structural equation models with several misspecifications of each model. Results suggested several unique findings. First, increasing numbers of omitted paths in the measurement model were associated with decreasing numbers of improper solutions. Second, bias in the parameter estimates was higher in samples with improper solutions than in samples including only proper solutions. Third, investigations of the consequences of using constrained estimates in the presence of improper solutions indicated that inequality constraints helped some samples achieve convergence. Finally, the use of confidence intervals as well as four other proposed tests yielded similar results when testing whether the error variance was greater than or equal to zero.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:29:y:2001:i:4:p:468-508

DOI: 10.1177/0049124101029004003

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