Assessing Cutoff Values of SEM Fit Indices: Advantages of the Unbiased SRMR Index and Its Cutoff Criterion Based on Communality

ABSTRACT

Holding model misspecification constant, the behavior of fit indices depends on factors such as the number of variables being modeled (model size), and the average observed correlation (magnitude of factor loadings or measurement quality). We examine by simulation the interplay of these factors with sample size in CFA models. When a biased estimator of the fit index is used (CFI, TLI, or GFI), the behavior of the sample indices depends on sample size, rendering establishing cutoff values impossible. When an unbiased estimator is used (SRMR, or RMSEA) the behavior of the indices matches that of the population parameter and depends on the average R² of the observed variables (communality); and for the RMSEA, also on model size. The use of the unbiased SRMR with a cutoff value adjusted by R² is recommended as it enables assessing the degree of a model misspecification across model size, sample size, and measurement quality.

KEYWORDS:

• Structural equation modeling (SEM)
• goodness-of-fit indices
• magnitude of factor loadings
• reliability paradox

Acknowledgments

We thank the Research Computing Center at the University of South Carolina for providing the computing resources that contributed to the results of this paper.

Disclosure statement

We have no known conflict of interest to disclose.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

¹ For good measure, we also include the biased SRMR in our study.

² Smaller values of the CFI and GFI indicate poorer fit, whereas larger values of the RMSEA and SRMR indicate poorer fit.

³ Presently the unbiased SRMR index and its confidence intervals and tests of close fit are available on the lavaan package version 0.6–7 in R (see function lavResiduals).

Additional information

Funding

This work was supported by the National Science Foundation under Grant No. SES-1659936, by the Research Center for Child Well-Being (NIGMS P20GM130420) and by a Salvador de Madariaga Grant No. PRX18/00297, and Grant No. PGC2018-093838-B-I00 from the Spanish Ministerio de Ciencia, Innovación y Universidades.