Confirmatory Factor Analysis (CFA)
Confirmatory Factor Analysis · Also known as: Doğrulayıcı Faktör Analizi (CFA), confirmatory factor analysis, measurement model
Confirmatory factor analysis tests whether a researcher-specified factor structure fits the observed data. Formalised by Karl Jöreskog in 1969, it is the measurement-model step within structural equation modelling and is the standard tool for validating the factorial structure of scales and questionnaires before comparing groups or estimating latent relationships.
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When to use it
CFA is appropriate when you have a theoretically motivated or previously explored factor structure that you want to validate on a new sample. A minimum sample of 200 is generally required — a common guideline is 5–10 observations per estimated parameter. Indicators should be continuous or ordinal (using polychoric correlations for the latter), and the data should approximate multivariate normality, or a robust estimator should be used. The correlation matrix must be factorable (KMO ≥ 0.60; Bartlett's test significant). When comparing latent constructs across groups, measurement invariance must be verified first.
Strengths & limitations
- Directly tests a theoretically specified factor structure rather than discovering one from the data, making findings far more interpretable and reproducible.
- Provides a comprehensive set of model fit indices (CFI, RMSEA, SRMR) that quantify how well the proposed structure matches the observed covariances.
- Serves as the foundation for structural equation modelling, enabling researchers to estimate latent relationships with measurement error explicitly modelled.
- Supports formal measurement invariance testing, allowing rigorous group comparisons of latent constructs.
- Requires a well-specified a priori factor structure; without prior theory or an exploratory stage the researcher risks an arbitrarily constrained model.
- Sensitive to sample size: at n < 200 fit indices become unstable and parameter estimates unreliable; complex models need substantially larger samples.
- Assumes multivariate normality under standard ML estimation; non-normality inflates the chi-square statistic and biases fit indices unless a robust estimator is used.
- Model fit indices are global and can mask local misfit; a model may show acceptable overall fit while some specific indicator relationships are poorly reproduced.
Frequently asked
What is the difference between CFA and EFA?
EFA is exploratory: it discovers how many factors underlie a set of items and which items belong to which factor, without any prior specification. CFA is confirmatory: the researcher specifies the factor structure in advance — which items load on which factors, and which cross-loadings are fixed to zero — and then tests whether that structure fits the data. A common and recommended workflow is to use EFA on one sample to discover the structure, then use CFA on a second, independent sample to confirm it.
Which fit indices should I report?
Report at least one absolute fit index (RMSEA with its 90% confidence interval, and SRMR) and at least one incremental fit index (CFI or TLI). The conventional cutoffs established by Hu and Bentler (1999) are CFI ≥ 0.95, RMSEA ≤ 0.06, and SRMR ≤ 0.08. The chi-square test should also be reported but interpreted cautiously, as it is highly sensitive to sample size.
When do I need to test measurement invariance?
Whenever you want to compare latent factor means, variances, or relationships across two or more groups — for example, across genders, cultures, or time points. The sequence is configural invariance (same pattern of free and fixed loadings), then metric invariance (equal loadings), then scalar invariance (equal item intercepts). Only at scalar invariance can latent mean comparisons be made meaningfully.
How large a sample do I need?
A minimum of 200 cases is the commonly cited threshold, but the real requirement is tied to model complexity. A widely used rule of thumb is 5–10 observations per free parameter. Simple models with strong loadings can perform reasonably with around 100–150 cases, while complex multi-factor or multi-group models may need 400 or more.
Sources
- Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). The Guilford Press. ISBN: 978-1462515363
- Hu, L. & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. DOI: 10.1080/10705519909540118 ↗
How to cite this page
ScholarGate. (2026, June 1). Confirmatory Factor Analysis. ScholarGate. https://scholargate.app/en/statistics/cfa
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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