Single-Level Bifactor Models as Implicit Multilevel Factor Models Without a Bifactor Structure

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.