In psychological research the data are frequently ordered categorical (e.g., data collected using Likert scales). Hu and Bentler cautioned that the suggested cutoff values might not generalize to conditions that were not manipulated in their study, nor to estimation methods other than ML. However, Hu and Bentler’s study only concerns continuous data that are analyzed using the normal-theory maximum likelihood (ML). Hu and Bentler’s study has become highly influential, and their recommended cutoffs have been adopted in many SEM practices. 95 indicate relatively good model–data fit in general. Hu and Bentler suggested that an RMSEA smaller than. To address the lack of statistical justification of these recommendations, Hu and Bentler ( 1999) conducted a simulation study to investigate the rejection rates under correct and misspecified models, by applying various cutoff values for many fit indices, including RMSEA, CFI, and TLI. However, these suggestions are largely based on intuition and experience rather than on any statistical justification (see Marsh, Hau, & Wen, 2004). Earlier research (e.g., Browne & Cudeck, 1993 Jöreskog & Sörbom, 1993) suggested that an RMSEA value of. The application of RMSEA, CFI, and TLI is heavily contingent on a set of cutoff criteria. Discussions regarding the use of RMSEA, CFI, and TLI for ordered categorical data are given. Applying the conventional cutoffs to DWLS and ULS, therefore, has a pronounced tendency not to discover model–data misfit. 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. Both simulated and empirical polychoric correlation matrices with various degrees of model misspecification were employed to address the above question. 08), what is the RMSEA value when ULS or DWLS is applied? CFI and TLI were investigated in the same fashion. 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. 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. 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. 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.