Understanding the Model Size Effect on SEM Fit Indices

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 sam...

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Bibliographic Details
Published in:Educational and psychological measurement Vol. 79; no. 2; pp. 310 - 334
Main Authors: Shi, Dexin, Lee, Taehun, Maydeu-Olivares, Alberto
Format: Journal Article
Language:English
Published: Los Angeles, CA SAGE Publications 01.04.2019
SAGE PUBLICATIONS, INC
Subjects:
Goodness of Fit
Indexes
Population
Sample Size
Specification
Structural equation modeling
Structural Equation Models
Variables
fit indices
model size effect
structural equation modeling (SEM)
ISSN:0013-1644, 1552-3888, 1552-3888
Online Access:Get full text
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Summary: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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ISSN:0013-1644
1552-3888
1552-3888
DOI:10.1177/0013164418783530