Calculating and Interpreting Maximal Reliability in Bifactor Models

Confirmatory bifactor models have been widely applied to understand multidimensional constructs in different areas of psychology research. Maximal reliability captures how well an optimal linear composite (OLC) represents the target latent variable. In this article, we point out that researchers have been using an incorrect generalization of coefficient H, a maximal reliability coefficient developed for one-factor models, with bifactor models. We present two sets of correct equations for maximal reliability: one based on an OLC for the entire scale and one based on a sub-composite consisting only of relevant items (OLSC). We illustrate these equations on a simulated data example and on a real data example, and compare them to other reliability coefficients. In a small population simulation, we find that OLCs and OLSCs are not reliable measures of group factors in models that contain fewer than 100 indicators. In addition, somewhat unexpectedly, we find that OLCs and OLSCs often receive negative weights. Overall, we recommend against using optimal composites or sub-composites as proxies for group factors, due to poor reliability and difficulties of interpretation. However, maximal reliability indices can be reported to evaluate the quality of a bifactor model.