Understanding the Model Size Effect on SEM Fit Indices
2018/06/29 by Dexin Shi, Taehun Lee, Alberto Maydeu-Olivares +1 · 910 citations
Materials Science · Mathematics · Physics and Astronomy · Psychology · #Econometrics #Electron and X-Ray Spectroscopy Techniques #Goodness of fit #Machine Learning in Materials Science #Mathematics #Psychology #Statistics #Surface and Thin Film Phenomena
paper · pdf · doi:10.1177/0013164418783530
published in Educational and Psychological Measurement 79(2), 310-334 (SAGE Publishing)
openalex publication_date 2018/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract
This study investigated the effect the number of observed variables ( p) has on three structural equation modeling indices: the comparative fit index (CFI), the Tucker–Lewis index (TLI), and the root mean square error of approximation (RMSEA). The behaviors of the population fit indices and their sample estimates were compared under various conditions created by manipulating the number of observed variables, the types of model misspecification, the sample size, and the magnitude of factor loadings. The results showed that the effect of p on the population CFI and TLI depended on the type of specification error, whereas a higher p was associated with lower values of the population RMSEA regardless of the type of model misspecification. In finite samples, all three fit indices tended to yield estimates that suggested a worse fit than their population counterparts, which was more pronounced with a smaller sample size, higher p, and lower factor loading.
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