Dynamic Fit Index Cutoffs for Confirmatory Factor Analysis Models

Model fit assessment is a central component of evaluating confirmatory factor analysis models and the validity of psychological assessments. Fit indices remain popular and researchers often judge fit with fixed cutoffs derived by Hu and Bentler (1999). Despite their overwhelming popularity, methodological studies have cautioned against fixed cutoffs, noting that the meaning of fit indices varies based on a complex interaction of model characteristics like factor reliability, number of items, and number of factors. Criticism of fixed cutoffs stems primarily from the fact that they were derived from one specific confirmatory factor analysis model and lack generalizability. To address this, we propose a simulationbased method called dynamic fit index cutoffs such that derivation of cutoffs is adaptively tailored to the specific model and data characteristics being evaluated. Unlike previously proposed simulation-based techniques, our method removes existing barriers to implementation by providing an open-source, Web based Shiny software application that automates the entire process so that users neither need to manually write any software code nor be knowledgeable about foundations of Monte Carlo simulation. Additionally, we extend fit index cutoff derivations to include sets of cutoffs for multiple levels of misspecification. In doing so, fit indices can more closely resemble their originally intended purpose as effect sizes quantifying misfit rather than improperly functioning as ad hoc hypothesis tests. We also provide an approach specifically designed for the nuances of 1-factor models, which have received surprisingly little attention in the literature despite frequent substantive interests in unidimensionality.