Issues in Estimating Interpretable Lower Order Factors in Second-Order Hierarchical Models: Commentary on Clark et al. (2021)

Abstract

In a previous issue of Clinical Psychological Science, Clark and colleagues asserted that lower order factors in second-order models are comparable with specific factors in bifactor models when residualized on the general factor. Modeling simulated data demonstrated that residualized lower order factors are correlated with bifactor-specific factors only to the extent that factor loadings are proportional. Modeling actual data with violations of proportionality showed that specific and residualized lower order factors are not always highly correlated and have differential correlations with criterion variables even when both models fit acceptably. Because proportionality constraints limit only second-order models, bifactor models should be the first option for hierarchical modeling.