Bifactor Model (General and Specific Factors)
Bifactor Measurement Model · Also known as: Bifaktör Modeli — Genel ve Spesifik Faktörler, hierarchical factor model, general-specific factor model, Schmid-Leiman model
The bifactor measurement model specifies that every indicator loads simultaneously on a single general factor and on one of several specific (group) factors. Formally introduced by Holzinger and Swineford in 1937 and brought into mainstream psychometrics by Reise (2012), it is now the standard tool for evaluating whether a multidimensional scale can legitimately yield a single composite score.
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When to use it
The bifactor model is appropriate when you have a multidimensional scale whose items cluster into two or more meaningful subscales, yet you also want to justify reporting a total (composite) score. The minimum practical sample size is 200 cases, and each factor — general and specific — should have at least three indicators; with fewer than five items overall the model becomes under-identified and will not converge. Indicators should be measured at an ordinal or continuous level; if items are ordinal, a polychoric correlation matrix and a WLS estimator are preferred. Normality of the observed variables is not required. The key substantive condition is the assumption that a single latent general factor genuinely runs through all items: if domain knowledge does not support this — for example, a battery combining logically unrelated constructs — the bifactor structure is not appropriate and a correlated-factors CFA should be used instead.
Strengths & limitations
- Simultaneously models a general latent factor and specific subdomain factors within a single, identifiable measurement model.
- Provides ωh, the most direct psychometric evidence for the defensibility of a composite total score on a multidimensional scale.
- ECV and ωh together allow researchers to quantify and report the degree of unidimensionality without forcing an implausible one-factor restriction.
- Subsumes and generalises the Schmid-Leiman orthogonalisation of hierarchical models, producing loadings that are directly interpretable without orthogonalisation as a separate step.
- Requires a sample of at least 200 — in practice 300 or more for stable estimates — making it unsuitable for small or pilot studies.
- A minimum of three indicators per factor (general and each specific) is necessary for identification; thin subscales with one or two items cannot be accommodated.
- Model estimation can fail to converge or produce non-positive-definite factor correlation matrices when the bifactor structure is misspecified or when specific factors are very weakly defined.
- The orthogonality constraint between general and specific factors is a model assumption, not an empirical finding; if the true structure involves correlated factors, the bifactor parameterisation may distort the loadings.
Frequently asked
What is the difference between a bifactor model and a second-order CFA?
In a second-order (hierarchical) CFA, the general factor influences items only indirectly: it predicts the first-order specific factors, which in turn predict the items. In the bifactor model, the general factor influences every item directly and simultaneously alongside the specific factors. The practical implication is that the bifactor model directly quantifies each item's general loading, making ECV and ωh calculable in a straightforward way, whereas second-order models require the Schmid-Leiman orthogonalisation step to obtain equivalent quantities.
What does omega-hierarchical (ωh) tell me?
ωh is the proportion of total score variance (across all items summed) that is attributable to the single general factor. A value of 0.50 or above is often cited as the threshold at which the general factor explains enough variance to make the composite score a meaningful, interpretable quantity. Values below 0.50 suggest the composite score is dominated by specific-factor variance and may be misleading as a summary of a single construct.
What is ECV and why does it matter?
ECV (Explained Common Variance) is the proportion of total common factor variance (the variance shared among items) that is accounted for by the general factor. It answers the question 'of all the variance that factors explain, how much is general?' Values of 0.70 or above indicate that the general factor is the dominant source of common variance, which is a necessary — though not sufficient — condition for defending a composite score.
How large a sample do I need?
The registry minimum is 200, but empirical simulation studies suggest that reliable convergence and stable parameter estimates typically require 300 or more cases, especially when specific factors are defined by only three items. With samples below 100 the model is unlikely to converge, and if it does, the standard errors will be untrustworthy. Bootstrap confidence intervals for ωh should be reported whenever the sample is under 500.
Sources
- Reise, S. P. (2012). The Rediscovery of Bifactor Measurement Models. Multivariate Behavioral Research, 47(5), 667–696. DOI: 10.1080/00273171.2012.715555 ↗
- Rodriguez, A., Reise, S. P. & Haviland, M. G. (2016). Evaluating Bifactor Models: Calculating and Interpreting Statistical Indices. Psychological Methods, 21(2), 137–150. DOI: 10.1037/met0000045 ↗
How to cite this page
ScholarGate. (2026, June 1). Bifactor Measurement Model. ScholarGate. https://scholargate.app/en/psychometrics/bifactor-model
Which method?
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