Small but Nontrivial: A Comparison of Six Strategies to Handle Cross-Loadings in Bifactor Predictive Models

The bifactor model is a promising alternative to traditional modeling techniques for studying the predictive validity of hierarchical constructs. However, no study to date has systematically examined the influence of cross-loadings on the estimation of regression coefficients in bifactor predictive models. Therefore, we present a systematic examination of the statistical performance of six modeling strategies to handle cross-loadings in bifactor predictive models: structural equation modeling (SEM), exploratory structural equation modeling (ESEM) with target rotation, Bayesian structural equation modeling (BSEM), and each of the three with augmentation. Results revealed four clear patterns: 1) forcing even small cross-loadings to zero was detrimental to empirical identification, estimation bias, power and Type I error rates; 2) the performance of ESEM with target rotation was unexpectedly weak; 3) augmented BSEM had satisfactory performance in an absolute sense and outperformed the other five strategies across most conditions; 4) augmentation improved the performance of ESEM and SEM, although the degree of improvement was not as substantial as that of BSEM. In addition, we also presented an empirical example to show the feasibility of the proposed approach. Overall, these findings can help users of bifactor predictive models design better studies, choose more appropriate analytical strategies, and obtain more reliable results. Implications, limitations, and future directions are discussed.

Automated summary

This study systematically examines the influence of cross-loadings on regression coefficient estimation in bifactor predictive models. Results reveal that forcing cross-loadings to zero has negative effects on model identification, estimation bias, power, and Type I error rates. ESEM with target rotation performs unexpectedly poorly, while augmented BSEM outperforms other strategies in most conditions. The empirical example demonstrates the feasibility of the proposed approach. These findings can assist users in designing better studies, selecting appropriate analytical strategies, and obtaining more reliable results when using bifactor predictive models.