Structural Equation Modeling with Small Samples: Test Statistics

1999/04/01 by Peter M. Bentler, Ke-Hai Yuan, Ke‐Hai Yuan · 619 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Modeling Techniques #Computer science #Covariance #Econometrics #Estimator #Mathematics #Monte Carlo method #Multivariate statistics #Psychometric Methodologies and Testing #Sample (material) #Sample size determination #Statistic #Statistical hypothesis testing #Statistics #Structural equation modeling #Test statistic

paper · doi:10.1207/s15327906mb340203

published in Multivariate Behavioral Research 34(2), 181-197 (Taylor & Francis)

openalex publication_date 1999/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Structural equation modeling is a well-known technique for studying relationships among multivariate data. In practice, high dimensional nonnormal data with small to medium sample sizes are very common, and large sample theory, on which almost all modeling statistics are based, cannot be invoked for model evaluation with test statistics. The most natural method for nonnormal data, the asymptotically distribution free procedure, is not defined when the sample size is less than the number of nonduplicated elements in the sample covariance. Since normal theory maximum likelihood estimation remains defined for intermediate to small sample size, it may be invoked but with the probable consequence of distorted performance in model evaluation. This article studies the small sample behavior of several test statistics that are based on maximum likelihood estimator, but are designed to perform better with nonnormal data. We aim to identify statistics that work reasonably well for a range of small sample sizes and distribution conditions. Monte Carlo results indicate that Yuan and Bentler's recently proposed F-statistic performs satisfactorily.

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