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

Clark and colleagues asserted that lower-order factors in second-order models are comparable to specific factors in bifactor models when residualized on the general factor (Clark et al., 2021). 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.