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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Single-Level Bifactor Models as Implicit Multilevel Factor Models Without a Bifactor Structure.

Christian L L Strauss1, Kristopher J Preacher1

  • 1Department of Psychology and Human Development, Vanderbilt University Peabody College, Nashville, TN, USA.

Multivariate Behavioral Research
|May 1, 2026
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Summary
This summary is machine-generated.

Bifactor models may incorrectly appear as the best fit for clustered data due to ignored hierarchical structures. Researchers should consider multilevel models for accurate factor interpretation in social and organizational research.

Keywords:
Bifactor modelconfirmatory factor analysismeasurement modelsmultilevel confirmatory factor analysis

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Area of Science:

  • Psychometrics
  • Multilevel Modeling
  • Structural Equation Modeling

Background:

  • Bifactor structures are frequently favored in measurement modeling.
  • Unmodeled clustering of observations within larger units (e.g., students in schools) may contribute to this preference.
  • The overlap between bifactor confirmatory factor analysis (CFA) and multilevel CFA warrants investigation.

Purpose of the Study:

  • To explore how unmodeled data clustering influences the preference for bifactor structures.
  • To investigate the structural symmetries and differences between bifactor CFA and multilevel CFA.
  • To demonstrate how ignoring clustering can lead to artifactual bifactor solutions and misinterpretations.

Main Methods:

  • Comparative analysis of bifactor confirmatory factor models and multilevel confirmatory factor analysis.
  • Simulation studies using identically structured data formats.
  • Empirical data analysis to validate simulation findings.

Main Results:

  • Bifactor solutions can emerge as artifacts when level-1 and level-2 effects are conflated in clustered data.
  • Ignoring clustering leads to inflated general factor loadings in bifactor models, favoring misspecified solutions.
  • Specific patterns of inflation were observed when fitting bifactor models to data with one level-2 factor and multiple level-1 factors.

Conclusions:

  • Researchers should consider multilevel measurement models as potential explanations for observed bifactor solutions.
  • Accurate interpretation of factors requires accounting for the hierarchical structure of data.
  • Failure to model data clustering can result in invalid factor interpretations.