Empirical Underidentification with the Bifactor Model: A Case Study

Bifactor models are commonly used to assess whether psychological and educational constructs underlie a set of measures. We consider empirical underidentification problems that are encountered when fitting particular types of bifactor models to certain types of data sets. The objective of the article was fourfold: (a) to allow readers to gain a better general understanding of issues surrounding empirical identification, (b) to offer insights into empirical underidentification with bifactor models, (c) to inform methodologists who explore bifactor models about empirical underidentification with these models, and (d) to propose strategies for structural equation model users to deal with underidentification problems that can emerge when applying bifactor models.