Last updated: 2019-05-17
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This study is a continuation from R. Noah Padgett’s Master’s Thesis. The project is generally about the performance of commonly used fit statistics in multilevel CFA models. The work is part of a large simulation study that will be reported in multiple manuscripts throughout the next year. This study is solely on the FIT statistis.
The ability of commonly used fit statistics to discriminate between a correctly specified model and misspecified models was investigated within a multilevel factor analysis context. Performance of fit statistics was investigated with receiver-operating-characteristics (ROC) analyses. Combining ROC analyses with traditional methods of investigating fit statistic performance resulted in converging evidence for the utility of the investigated fit statistics. Optimal thresholds were identified and found to vary across different robust estimation methods (i.e., MLR, ULSMV, and WLSMV). Estimation method and sample size were found to influence the performance of common fit statistic to detect misspecification of the level-1 model, while all fit statistics investigated performed poorly for detecting misspecification of the level-2 model. Recommendations were given for which commonly reported fit statistics to use, cut-off criteria to use for which estimators, and cautions about the use of the suggested cut-off criteria.