Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives

1999/01/01 by Li‐tze Hu, Peter M. Bentler · 88 citations
Decision Sciences · Mathematics · #Psychometric Methodologies and Testing #Cutoff #Statistics #Mathematics #Index (typography) #Population #Covariance #Structural equation modeling #Econometrics #Demography #Physics #Computer science

paper · doi:10.1080/10705519909540118

openalex publication_date 1999/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and Gamma Hat; a cutoff value close to .90 for Mc; a cutoff value close to .08 for SRMR; and a cutoff value close to .06 for RMSEA are needed before we can conclude that there is a relatively good fit between the hypothesized model and the observed data. Furthermore, the 2‐index presentation strategy is required to reject reasonable proportions of various types of true‐population and misspecified models. Finally, using the proposed cutoff criteria, the ML‐based TLI, Mc, and RMSEA tend to overreject true‐population models at small sample size and thus are less preferable when sample size is small.

Citations

• Single Sample Cross-Validation Indices for Covariance Structures
• Alternative Ways of Assessing Model Fit
• A Reliability Coefficient for Maximum Likelihood Factor Analysis
• Comparative fit indexes in structural models.
• The Analysis of Covariance Structures
• A General Approach to Confirmatory Maximum Likelihood Factor Analysis
• Testing Structural Equation Models.
• Factor Analysis and AIC

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