Assessing the Size of Model Misfit in Structural Equation Models

2017/02/07 by Alberto Maydeu-Olivares, Alberto Maydeu‐Olivares · 179 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Modeling Techniques #Algorithm #Confidence interval #Econometrics #Goodness of fit #Mathematics #Psychometric Methodologies and Testing #Residual #Sample size determination #Statistical hypothesis testing #Statistics #Strictly standardized mean difference #Structural equation modeling #Studentized residual

paper · doi:10.1007/s11336-016-9552-7

published in Psychometrika 82(3), 533-558 (Springer Science+Business Media)

openalex publication_date 2017/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

When a statistically significant mean difference is found, the magnitude of the difference is judged qualitatively using an effect size such as Cohen's d. In contrast, in a structural equation model (SEM), the result of the statistical test of model fit is often disregarded if significant, and inferences are drawn using "close" models retained based on point estimates of sample statistics (goodness-of-fit indices). However, when a SEM cannot be retained using a test of exact fit, all substantive inferences drawn from it are suspect. It is therefore important to determine the size of the model misfit. Standardized residual covariances and residual correlations provide standardized effect sizes of the misfit of SEM models. They can be summarized using the Standardized Root Mean Squared Residual (SRMSR) and the Correlation Root Mean Squared Residual (CRMSR) which can be used as overall effect sizes of the misfit. Statistical theory is provided that allows the construction of confidence intervals and tests of close fit based on the SRMSR and CRMSR. It is hoped that the use of standardized effect sizes of misfit will help reconcile current practices in SEM and elsewhere in statistics.

Citations

• Multidimensionality and Structural Coefficient Bias in Structural Equation Modeling
• Single Sample Cross-Validation Indices for Covariance Structures
• Structural Model Evaluation and Modification: An Interval Estimation Approach

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