Path analysis (observed only)

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Sem (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.

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Tests a hypothesised system of directed relationships among OBSERVED variables all at once (path analysis).

Path analysis estimates all direct and indirect effects in a specified diagram simultaneously with overall fit indices — like several regressions solved together, for measured (not latent) variables.

Worked example

Does stress affect performance directly and via sleep?

A path model with stress → sleep → performance (plus stress → performance) was fit to observed scores (n = 300).

Result

Sleep partially mediated the stress→performance effect (indirect effect = −.16; a = −.45, b = .35).

How you'd report it (APA)

A path analysis showed sleep partially mediated the effect of stress on performance, indirect effect = −.16.

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

When to use it

  • A system of directed effects among measured variables
    Several regressions that share variables, solved together. e.g. stress → sleep → performance with a direct stress → performance path.
  • You want direct AND indirect effects at once
    Path analysis decomposes total effects into direct and mediated parts within one model.
  • Every construct is a single observed score
    No latent variables — each node is one measured variable or a composite.

When NOT to — use instead

  • Constructs have multiple indicators
    If a construct is measured by several items, model it as latent to correct for measurement error. → Full SEM
  • A single X→M→Y triple
    One mediator with one path is simpler run as mediation. → Simple mediation

Hypotheses

H₀: the specified path model reproduces the observed covariances — model-implied and observed covariance matrices do not differ (exact fit).
Hₐ: the model does not fit; observed covariances depart from those the diagram implies. Judged by χ² and approximate-fit indices (CFI, RMSEA, SRMR), alongside the individual path estimates.

Parameter tested: all direct and indirect path coefficients in the diagram, plus overall fit indices (χ², CFI, RMSEA, SRMR)

Assumptions (and what to do if they fail)

The diagram is specified in advancehigh

Check: Paths come from theory. Adding paths until χ² passes is fitting noise.

If violated: Fit indices become meaningless; the model describes this sample, not the process.

No omitted common causeshigh

Check: Any variable that drives two nodes but is left out biases the paths between them.

If violated: Path coefficients absorb the confounding and are over- or under-stated.

Adequate sample for the number of pathsmedium

Check: Fit indices and SEs are unreliable at small n relative to the number of estimated paths.

If violated: RMSEA and χ² mislead; CIs are too narrow to trust.

Approximately multivariate-normal, linear relationsmedium

Check: Default ML estimation assumes it; check for gross non-normality and non-linearity.

If violated: Use a robust estimator, or the χ² and SEs are off.

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