Confirmatory FA

Verified

Multivariate (legacy hub)

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Or use your own dataset

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Tests a HYPOTHESISED measurement model where each item is specified to load on one (or more) named latent factor.

Reports the full fit-index battery: χ² + df + p, CFI, TLI, RMSEA + 90% CI, SRMR, AIC, BIC. Per-factor loadings + standard errors + 95% CIs; per-item residual variances; factor-correlation matrix; modification indices (with warning that data-driven re-specification capitalises on chance). The standard tool for validating a pre-specified factor structure on a confirmatory sample.

Worked example

Does the hypothesised three-factor structure fit the data?

A confirmatory factor analysis tested a pre-specified 3-factor model on 21 items (n = 400).

Result

The model fit well, χ²(186) = 342, CFI = .96, TLI = .95, RMSEA = .046 [.039, .053], SRMR = .045; all loadings exceeded .60.

How you'd report it (APA)

A CFA supported the three-factor structure, CFI = .96, RMSEA = .046, SRMR = .045.

When to use it

  • Validate an existing scale on a new sample
    Big Five Inventory (44 items, 5 factors) tested on a Vietnamese-adapted version (n=600).
  • Post-EFA confirmation on holdout sample
    EFA on development sample (n=300) yielded a 4-factor structure for a new wellbeing scale.

When NOT to — use instead

  • Factor structure unknown — exploratory analysis
    CFA tests a HYPOTHESISED model. → Exploratory FA
  • Sample too small (n < 200, or n < 5 × parameters)
    CFA fit indices are unstable on small samples. → Exploratory FA
  • Single-factor measurement model
    Single-factor CFA is essentially a test of unidimensionality. → McDonald's Omega
  • Multi-group invariance comparison
    Use measurement_invariance — the configural→metric→scalar→strict ladder. → Measurement Invariance

Assumptions (and what to do if they fail)

Items measured on a continuous / Likert scalemedium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

A pre-specified factor structure (lavaan-style syntax)medium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Approximately multivariate-normal residuals (for ML)medium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Listwise exclusion of incomplete response setsmedium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Ready to run a Confirmatory FA on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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