Dynamic Fit Index Cutoffs for Treating Likert Items as Continuous

Recent reviews report that about 80% of empirical factor analyses are applied to Likert-type responses and that it is exceedingly common to treat Likert-type item responses as continuous. However, traditional model fit index cutoffs like RMSEA ≤ .06 or CFI ≥ .95 were derived to have 90+% sensitivity to misspecification with continuous responses. A disconnect therefore emerges whereby traditional methodological guidelines assume continuous responses whereas empirical data often contain Likert-type responses. We provide an illustrative simulation study to show that this disconnect is not innocuous—sensitivity of traditional cutoffs to misspecification is close to 100% with continuous responses but can fall considerably if 5-point Likert responses are treated as continuous in some conditions. In other conditions, the reverse may occur, and traditional cutoffs may be too strict. Generally, applying traditional cutoffs to Likert-type responses can adversely impact conclusions about fit adequacy. This paper aims to address this prevalent issue by extending the dynamic fit index (DFI) framework to accommodate Likert-type responses. DFI is a simulation-based method that was initially intended to address changes in cutoff sensitivity to misspecification due to model characteristics (e.g., number of items, strength of loadings). Here, we propose extending DFI so that it also accounts for data characteristics (e.g., number of Likert scale points, response distribution) . Two simulations are included to demonstrate that – with 5-point Likert-type responses – the proposed method (a) improves upon traditional cutoffs, (b) improves upon DFI cutoffs based on multivariate normality, and (c) consistently maintains 90+% sensitivity to misspecification.