A Structural After Measurement Approach to Bifactor Predictive Models

The bifactor model is becoming a popular tool for modeling hierarchical constructs. However, the bifactor predictive model, which uses both the general factor and all group factors to predict a criterion, often encounters symptoms of empirical under-identification. The augmentation approach can effectively alleviate these issues, but it is not always feasible. There is a need for a more readily available approach. In the present study, we examined the extent to which the Structural After Measurement (SAM; Rosseel & Loh, 2022) approach can mitigate these statistical issues in bifactor predictive models. Monte Carlo simulations showed that, compared to the classic one-step Structural Equation Modeling (SEM) approach, SAM can effectively enhance the statistical performance of bifactor predictive models. This enhancement is evidenced by higher convergence rates, smaller RMSE, more accurate standard error estimates, better coverage rates, and improved control of Type I error rates, albeit at the cost of somewhat higher bias. Additionally, we demonstrated that combining the SAM approach with the augmentation approach resulted in the best performance across all simulated conditions. An empirical illustration was also provided to demonstrate the feasibility of the SAM approach.