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 RMSEAvalue (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
Behavior Research Methods – Springer Journals
Published: Jun 4, 2018
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