Confirmatory Factor Analysis
CFA online with chi square, RMSEA, CFI, TLI, SRMR, factor loadings and modification indices.
When to use it
Use confirmatory factor analysis (CFA) when a theoretical measurement model already specifies which observed indicators load on which latent factors and you want to test how well that model fits the data. Standard step in psychometric scale validation, in confirming a previously published factor structure on a new sample, and as the measurement-model layer of a full structural-equation model.
When NOT to use it
Do not use CFA when no a priori factor structure exists; run exploratory factor analysis (EFA) first. Do not use CFA on samples smaller than about 200 unless the model is very simple; chi-square and RMSEA become unreliable. Do not interpret a single fit index in isolation; report chi-square, RMSEA, CFI, and SRMR together. The full structural model among latent variables is outside this tool's scope.
What you get
Standardised factor loadings per indicator with their SEs and z-tests; factor variances and inter-factor correlations; fit indices: chi-square with df and p, RMSEA with 90 percent CI, CFI, TLI, SRMR; modification indices for the largest expected drops in chi-square if a constraint were freed; residual covariance matrix.
How to interpret the output
Conventional thresholds (Hu and Bentler 1999): RMSEA at or below 0.06, CFI at or above 0.95, SRMR at or below 0.08 indicate good fit; values up to 0.08 RMSEA, 0.90 CFI, 0.10 SRMR indicate acceptable fit. Standardised loadings of 0.5 or higher are conventionally meaningful. A significant chi-square in large samples is common and not by itself a rejection; rely on RMSEA, CFI, and SRMR jointly. Modification indices should only motivate model changes that are theoretically defensible.
Common pitfalls
- Adding correlated errors purely to chase fit indices without theoretical justification.
- Reporting only chi-square (which almost always rejects in large samples).
- Treating CFI alone as proof of good fit; report the full bundle.
- Confusing CFA with PCA or EFA; CFA is a confirmatory model with directed loadings.
Try it in StatVeda
The Confirmatory Factor Analysis (SEM subset) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Confirmatory Factor Analysis (SEM subset)References
- Hu, L. and Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis. Structural Equation Modeling, 6(1), 1 to 55.
- Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research, 2nd edition. Guilford Press, New York.
- Joreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183 to 202.