Improper Solutions in Structural Equation Models: Causes, Consequences, and Strategies
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.
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About 40/50 participants should be sufficient to find a reliable medium-sized mediation path in a longitudinal study with bootstrapping coefficients.
“As suggested in [38], to find a reliable medium-sized mediation path in a longitudinal study like our own with bootstrapping coefficients, about 40/50 participants should be sufficient.”
From Accept anxiety to improve sleep: The impact of the covid-19 lockdown on the relationships between mindfulness, distress and sleep quality (2021) · cites this paper as [38]
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“…restrictions), weak (i.e., equal loadings), strong (i.e., equal loadings and intercepts) and strict (i.e., equal loadings, intercepts and residuals) invariant models, were tested for statistical significance using the difference of the χ2-values (Chen et al., 2001; Cheung & Rensvold, 2002).”
MethodSilveira, S., Boney, S., Tapert, S. F., & Mishra, J. (2021) · doi:10.1101/2021.01.29.21250544
- Authors
- CHEN, F., BOLLEN, K. A., PAXTON, P., CURRAN, P. J., & KIRBY, J. B.
- Affiliations
- University of North Carolina at Chapel Hill (US)
- The Ohio State University (US)
- Agency for Healthcare Research and Quality (US)
- Venue
- Sociological Methods & Research
- Publisher
- SAGE Publications
- Published
- 2001-05
- Volume
- 29
- Issue
- 4
- Pages
- 468-508
- ISSN
- 0049-1241 (ISSN-L)
- 1552-8294
- OpenAlex
- W1971363185
- Cited by
- 512
- References
- 21
- Citations by year
- 2026: 28 · 2025: 16 · 2024: 24 · 2023: 24 · 2022: 32 · 2021: 44 · 2020: 22 · 2019: 33 · 2018: 18 · 2017: 24 · 2016: 25 · 2015: 21 · 2014: 24 · 2013: 15 · 2012: 15
- FWCI
- 12.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Sociological Methods & Research (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Keywords
- improper solutions, structural equation modeling, model misspecification, measurement model, inequality constraints, constrained estimation, convergence, confidence intervals, hypothesis testing
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