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

Bo Zhang, Jing Luo, Tianjun Sun, Mengyang Cao, Fritz Drasgow

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)115-132
JournalMultivariate Behavioral Research
Issue number1
StatePublished - 2023


  • augmentation
  • Bifactor predictive model
  • BSEM
  • cross-loadings
  • ESEM

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)


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