A Unification of Second-Order and Bi-Factor EFA

As empirical applications and methodological research on second-order exploratory factor analysis have matured, important refinements to estimation procedures, interpretive frameworks, and theoretical expectations have emerged. These advances establish second-order EFA as a rigorous alternative to bi-factor EFA and to conventional EFA models characterized by substantial factor correlations. We further demonstrate that bi-factor EFA models constitute a reparameterization of second-order EFA with direct effects, clarifying the formal relationship between these approaches. The unification of bi-factor and second-order EFA models reveals a novel rotation approach for bi-factor solutions that outperforms bi-geomin in simulation studies and yields more interpretable factor solutions in empirical studies.