Model Comparison

Verified

Factor Analysis

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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Compares competing models on fit versus parsimony to pick the best-supported one.

Reports the fit-index battery (χ², CFI, TLI, RMSEA, SRMR) and information criteria (AIC, BIC) to judge absolute fit and compare nested or non-nested models — better fit and lower AIC/BIC win.

Worked example

Does a one-factor or two-factor model fit better?

One- and two-factor CFA models were compared on fit indices and information criteria (n = 400).

Result

The two-factor model fit far better than the one-factor model (CFI = .99 vs .47) and was retained.

How you'd report it (APA)

Model comparison strongly favoured the two-factor model (CFI .99 vs .47).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Choosing among competing models
    Two or more specifications of the same data — you want the fit-index battery and information criteria side by side. e.g. one-factor vs two-factor CFA.
  • Balancing fit against parsimony
    AIC and BIC reward fit but penalise extra parameters, so a slightly worse-fitting simpler model can win.

When NOT to — use instead

Assumptions (and what to do if they fail)

Same data and sample for every modelhigh

Check: AIC/BIC are only comparable when the models are fit to the identical cases and variables (same N, no listwise-deletion differences).

If violated: A model that quietly dropped fewer cases looks better for the wrong reason — the criteria are not comparable.

Nested vs non-nested comparisonmedium

Check: Nested models can use a χ² difference test; non-nested ones rely on AIC/BIC and fit indices, not a significance test.

If violated: A χ² difference test applied to non-nested models is invalid.

Lower AIC/BIC is directional, not a testmedium

Check: Report the difference (ΔAIC/ΔBIC); a tiny gap is weak evidence even though one number is lower.

If violated: Declaring a winner on a trivial ΔAIC over-reads noise as a decision.

Ready to run a Model Comparison on your own data?

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

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