Why we need to abandon fixed cutoffs for goodness-of-fit indices: An extensive simulation and possible solutions

Abstract

To evaluate model fit in confirmatory factor analysis, researchers compare goodness-of-fit indices (GOFs) against fixed cutoff values (e.g., CFI > .950) derived from simulation studies. Methodologists have cautioned that cutoffs for GOFs are only valid for settings similar to the simulation scenarios from which cutoffs originated. Despite these warnings, fixed cutoffs for popular GOFs (i.e., χ2, χ2/df, CFI, RMSEA, SRMR) continue to be widely used in applied research. We (1) argue that the practice of using fixed cutoffs needs to be abandoned and (2) review time-honored and emerging alternatives to fixed cutoffs. We first present the most in-depth simulation study to date on the sensitivity of GOFs to model misspecification (i.e., misspecified factor dimensionality and unmodeled cross-loadings) and their susceptibility to further data and analysis characteristics (i.e., estimator, number of indicators, number and distribution of response options, loading magnitude, sample size, and factor correlation). We included all characteristics identified as influential in previous studies. Our simulation enabled us to replicate well-known influences on GOFs and establish hitherto unknown or underappreciated ones. In particular, the magnitude of the factor correlation turned out to moderate the effects of several characteristics on GOFs. Second, to address these problems, we discuss several strategies for assessing model fit that take the dependency of GOFs on the modeling context into account. We highlight tailored (or "dynamic") cutoffs as a way forward. We provide convenient tables with scenario-specific cutoffs as well as regression formulae to predict cutoffs tailored to the empirical setting of interest.