Confirmatory Factor Analysis for Scales
Confirmatory Factor Analysis Method for Scale Validation and Structural Testing · Also known as: CFA, Confirmatory factor analysis, Path analysis, Structural equation modeling
Confirmatory Factor Analysis (CFA) is a statistical method for testing whether a hypothesized factorial structure fits empirical data. Developed by Karl G. Jöreskog in 1969, CFA is the standard approach for validating psychometric scales by evaluating whether items load onto theoretically specified latent factors as expected. Unlike exploratory factor analysis, CFA requires a priori specification of the factor structure and provides goodness-of-fit indices to assess model adequacy.
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When to use it
CFA is appropriate for validating an established scale or testing a theoretically motivated factor structure in an independent sample. It is the standard approach in scale validation studies, cross-cultural equivalence testing, and longitudinal measurement invariance. CFA is less suited for exploratory scale development (use EFA instead) or when prior theory about scale structure is absent. Sample size requirements are substantial (typically 200–500+ respondents), limiting applicability in small populations.
Strengths & limitations
- Tests a priori hypotheses about scale structure, providing evidence for or against theoretical models
- Yields multiple fit indices facilitating nuanced model evaluation beyond simple pass/fail criteria
- Estimates factor correlations and measurement error, enabling comprehensive understanding of scale properties
- Allows testing of measurement invariance across groups (e.g., gender, age), ensuring equal scale functioning
- Requires large sample sizes (200–500+); small samples lead to unstable estimates and inflated Type II error rates
- Assumes data are approximately multivariate normal; violations (extreme non-normality, categorical responses) require robust methods
- Chi-square test is overly sensitive to minor model misspecification in large samples, occasionally rejecting well-fitting models
- Requires a priori specification; flexibility in post-hoc model modification risks capitalization on chance and inflated Type I error
Frequently asked
What is the minimum sample size for CFA?
A common recommendation is at least 200 respondents, with 300–500 preferred for better power. Some propose a ratio-based rule (10–20 participants per parameter estimated). Smaller samples (< 200) lead to unstable parameter estimates and inadequate power. Larger samples increase power to detect model misfit but may produce overly strict chi-square tests.
How do I compare two competing CFA models?
If models are nested (one is a constrained version of the other), use a chi-square difference test (Δχ²) with degrees of freedom equal to the difference in model df. Non-nested models are compared using information criteria (AIC, BIC). Additionally, examine practical differences in fit indices (e.g., ΔCFI, ΔRMSEA).
What if my CFA model does not fit the data well?
Examine modification indices and residual covariances to identify problematic areas. However, only modify the model if theoretically justified. Consider alternative factor structures, check data for outliers or violations of assumptions, or consult domain experts about construct definition. Re-collect data from a new sample to validate any changes.
Should I report all fit indices or just a few?
Report multiple fit indices: χ² with df and p-value, CFI, RMSEA with 90% CI, SRMR, and sample-size-adjusted indices if using large samples. This triangulation strengthens evidence for model fit. Relying on a single index (e.g., only χ² or only RMSEA) is insufficient and may lead to misinterpretation.
Sources
- Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183-202. DOI: 10.1007/BF02289343 ↗
- Hoyle, R. H. (Ed.). (2012). Handbook of Structural Equation Modeling. New York: Guilford Press. ISBN: 9781462503254
- Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling (4th ed.). New York: Guilford Press. ISBN: 9781462523344
How to cite this page
ScholarGate. (2026, June 3). Confirmatory Factor Analysis Method for Scale Validation and Structural Testing. ScholarGate. https://scholargate.app/en/psychometrics/confirmatory-factor-analysis-scale
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