Revisiting the Bi-Factor Model: Can Mixture Modeling Help Assess Its Applicability?

Abstract

This article revisits from the perspective of finite mixture modeling the increasingly popular bi-factor model applied in contemporary behavioral and social research. It is pointed out that in a population with substantial unobserved heterogeneity resulting from a mixture of latent classes, and where the unidimensional model holds along with models that markedly differ from the bi-factor model, the latter may turn out to be spuriously plausible. To raise caution about this possibility, an example of a 3-class setting is provided, where correspondingly (a) the single (global) factor model, (b) a model with a global factor and a single local factor, and (c) a model with a global factor and two local factors hold, while the bi-factor model with a global factor and three local factors is also plausible for the analyzed data overall. Examination of population heterogeneity prior to testing the bi-factor model is therefore recommendable in empirical research, in order to avoid spurious findings of its plausibility when ignoring substantial unobserved heterogeneity in studied populations.