Confirmatory Factor Analysis — Scale Validation (CFA)
Confirmatory Factor Analysis for Scale Validation · Also known as: Doğrulayıcı Faktör Analizi — Ölçek Doğrulama (CFA), confirmatory factor analysis, measurement model testing
Confirmatory factor analysis is a measurement modelling technique that tests whether a hypothesised factor structure — typically derived from theory or an earlier exploratory analysis — fits observed data from a new sample. Developed by Karl Jöreskog in 1969, it became the dominant tool for validating psychological scales because it requires the researcher to specify in advance which items belong to which latent factor and then assesses the adequacy of that specification against explicit statistical fit criteria.
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When to use it
CFA is appropriate when a factor structure has already been specified on theoretical or empirical grounds — most commonly after exploratory factor analysis has been conducted on a separate sample. It is the standard tool for validating a multi-item psychometric scale before using it in substantive research. Two conditions must be met. First, each factor must be identified: the conventional rule requires at least three indicators per factor, with the first loading fixed for scale-setting and at least two free parameters remaining per factor. Second, the sample must be large enough for maximum likelihood estimation to behave stably; a minimum of 150 cases is a widely cited lower bound, though complex models with many factors and items may require 300 or more. For ordinal Likert-type items, the WLSMV (weighted least squares mean-variance adjusted) estimator is preferred over ML because it does not assume multivariate normality of the response distribution.
Strengths & limitations
- Provides rigorous, quantitative tests of theoretically motivated factor structures rather than merely describing patterns in data.
- Yields multiple complementary fit indices that together give a nuanced picture of how well a proposed measurement model holds.
- Allows model comparison: nested models can be compared with chi-square difference tests, and non-nested models with AIC/BIC, enabling principled decisions about scale structure.
- Accommodates ordinal data through WLSMV estimation and polychoric correlation matrices without requiring normality.
- Requires that the factor structure be specified in full before seeing the new data; exploratory re-specification on the same sample inflates fit statistics and undermines the confirmatory logic.
- The chi-square test statistic is sensitive to sample size and virtually always rejects in large samples, making it uninformative in isolation.
- Modification indices can guide model improvements, but applying them without theoretical backing produces models that overfit the sample and do not generalise.
- Minimum sample requirements (n ≥ 150) are higher than for simpler reliability analyses, and complex models may demand considerably more.
Frequently asked
What is the difference between CFA and EFA?
EFA is exploratory: it estimates how many factors underlie a set of items and which items load on which factor, without any prior specification. CFA is confirmatory: the researcher specifies the complete factor pattern in advance and tests how well that fixed pattern reproduces the observed data. The standard workflow is to discover structure with EFA on one sample, then test that structure with CFA on a new, independent sample.
What fit values indicate a good-fitting model?
The most widely used thresholds, based on Hu and Bentler (1999), are CFI ≥ 0.95 and TLI ≥ 0.95 for incremental fit, RMSEA ≤ 0.06 with a confidence interval upper bound below 0.10, and SRMR ≤ 0.08. No single index is decisive; all should be reported together and interpreted in light of model complexity and sample size.
When should I use WLSMV instead of ML estimation?
Use WLSMV when your indicators are ordinal — for example, 5-point or 7-point Likert response scales. Maximum likelihood assumes that the items are continuous and multivariate normal; ordinal data violate this assumption, and ML produces biased parameter estimates and inflated fit statistics in that case. WLSMV works from a polychoric correlation matrix and adjusts the test statistic for the ordinal response format, yielding better-calibrated estimates.
Is it acceptable to free correlated residuals based on modification indices?
Only when there is a clear, theoretically motivated reason why two items share variance beyond the common factor — for example, two items with identical wording (method effect) or two items referring to the same narrow sub-facet. Freeing residual covariances merely to hit a CFI threshold without justification is post-hoc model fishing and produces results that are unlikely to replicate.
Sources
- Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). 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: A Multidisciplinary Journal, 6(1), 1–55. DOI: 10.1080/10705519909540118 ↗
How to cite this page
ScholarGate. (2026, June 1). Confirmatory Factor Analysis for Scale Validation. ScholarGate. https://scholargate.app/en/psychometrics/cfa-psychometric
Which method?
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