Patterns › Dimension reduction

Confirmatory factor analysis (CFA)

Confirmatory factor analysis tests a hypothesised item-to-factor structure, reporting fit indices, loadings and factor covariances.

What is Confirmatory factor analysis (CFA)?

CFA is the confirmatory counterpart of EFA: you specify which items load on which factors ('F1 =~ x1 + x2 + x3', one line per factor) and the model is tested against the observed covariance matrix. Factor covariances are estimated by default.

Identification uses the first-loading-fixed-to-1 convention, or standardized latents (all loadings free, factor variances fixed to 1) via the checkbox.

Same engine as the SEM analysis, restricted to the measurement model — see the SEM entry for estimation details.

When should I use Confirmatory factor analysis (CFA)?

  • Scale validation with a known factor structure.
  • Comparing theoretical measurement models via fit indices.
  • Preparing a measurement model before a structural SEM.

What data does it need?

Numeric indicator columns + factor definitions in the model syntax + estimator (ML / MLR / GLS) + missing-data handling + optional standardized latents.

What does it report?

Fit indices (χ², CFI, TLI, RMSEA + CI, SRMR, AIC, BIC), loadings with SE / z / p / CI / standardized values, factor covariances, R² per item.

What does it assume?

  • Multivariate normality for ML (MLR when doubtful).
  • Correctly specified structure.
  • Adequate n (≥ 10–20 per free parameter).

How do I interpret the result?

CFI/TLI ≥ 0.95, RMSEA ≤ 0.06, SRMR ≤ 0.08 = good fit; standardized loadings ≥ 0.5 desirable.

See also

References

  • Brown (2015). Confirmatory Factor Analysis for Applied Research.
  • Rosseel (2012). Structural Equation Modeling. JSS 48(2).