Single-Level Bifactor Models as Implicit Multilevel Factor Models Without a Bifactor Structure

It is well-known that bifactor structures are over-represented as preferred solutions in measurement modeling. This study explores the extent to which unmodeled clustering of observations in larger social or organization units (e.g., students clustered in schools) offers a partial explanation for this phenomenon. We investigate the overlap between bifactor confirmatory factor models and multilevel confirmatory factor analysis fit to identically structured data formats. Structural symmetries between these models are identified, leading to a series of postulates regarding expected differences across modeling frameworks. Next, through simulation and empirical data analysis, we demonstrate that bifactor solutions can emerge as artifacts of conflated level-1 and level-2 effects when clustering is ignored, causing invalid interpretations of factors. Specifically, results suggest that when bifactor models are fit to clustered data with one level-2 factor and multiple level-1 factors, general factor loadings are typically inflated, leading to greater support for the misspecified bifactor solution. We encourage researchers to consider multilevel measurement models as alternative explanations for bifactor solutions, so factors are accurately interpreted at the correct level of analysis.