RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods

In structural equation modeling, application of the root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) highly relies on the conventional cutoff values developed under normal-theory maximum likelihood (ML) with continuous data. For ordered categ...

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Bibliographic Details
Published in:Behavior research methods Vol. 51; no. 1; pp. 409 - 428
Main Authors: Xia, Yan, Yang, Yanyun
Format: Journal Article
Language:English
Published: New York Springer US 15.02.2019
Springer Nature B.V
Subjects:
Behavioral Science and Psychology
Brief Report
Cognitive Psychology
Continuous data
Data
Data processing
Indexes
Matrices
Nominal measurement
Psychology
Structural equation modeling
Ordered categorical data
Unweighted least squares
Fit index
Maximum likelihood
Structural equation modeling
Diagonally weighted least squares
ISSN:1554-3528, 1554-3528
Online Access:Get full text
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Summary:In structural equation modeling, application of the root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) highly relies on the conventional cutoff values developed under normal-theory maximum likelihood (ML) with continuous data. For ordered categorical data, unweighted least squares (ULS) and diagonally weighted least squares (DWLS) based on polychoric correlation matrices have been recommended in previous studies. Although no clear suggestions exist regarding the application of these fit indices when analyzing ordered categorical variables, practitioners are still tempted to adopt the conventional cutoff rules. The purpose of our research was to answer the question: Given a population polychoric correlation matrix and a hypothesized model, if ML results in a specific RMSEA value (e.g., .08), what is the RMSEA value when ULS or DWLS is applied? CFI and TLI were investigated in the same fashion. Both simulated and empirical polychoric correlation matrices with various degrees of model misspecification were employed to address the above question. The results showed that DWLS and ULS lead to smaller RMSEA and larger CFI and TLI values than does ML for all manipulated conditions, regardless of whether or not the indices are scaled. Applying the conventional cutoffs to DWLS and ULS, therefore, has a pronounced tendency not to discover model–data misfit. Discussions regarding the use of RMSEA, CFI, and TLI for ordered categorical data are given.
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ISSN:1554-3528
1554-3528
DOI:10.3758/s13428-018-1055-2