Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators

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Testing Measurement Invariance in Longitudinal Data with Ordered-Categorical Measures (2016, neutral): “In the only study to date, Sass et al. (2014) found that changes in practical fit indices performed poorly with DWLS estimation with mean- and variance-adjustments to the goodness-of-fit test statistic, especially for misspecified models.”
RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods (2018, methodology): “In a similar context, Sass, Schmitt, and Marsh (2014) suggested that the differences in CFIS and TLIS between nested models should be applied with caution, particularly for misspecified models, because these variables’ performance is impacted by both sample size and model complexity.”
Conducting Measurement Invariance Tests with Ordinal Data: A Guide for Social Work Researchers (2015, methodology): “Unresolved Issues in Invariance Testing with Ordinal Data A recent analysis identified limitations of all commonly used fit measures (Sass et al., 2014), but concluded that Δχ(2) may be the best choice with robust WLS estimation (Sass, 2011; Sass et al.”