Full SEM (latents + structural)

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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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The full structural equation model — latent constructs (a measurement model) plus the structural paths among them, estimated together.

Full SEM combines a CFA measurement model with regression-style paths among the latent variables, correcting relationships for measurement error and giving overall fit indices.

Worked example

Does latent job stress reduce latent performance via latent burnout?

A full SEM with three latent constructs (each with several indicators) and structural paths was fit (n = 350).

Result

Stress raised burnout (β = .52) which lowered performance (β = −.44); the model fit well (CFI = .96, RMSEA = .048) and the indirect effect was significant.

How you'd report it (APA)

A full SEM showed job stress reduced performance via burnout (indirect path significant), CFI = .96, RMSEA = .048.

When to use it

  • Latent constructs with multiple indicators
    Each construct is measured by several items, and you want the relationships among the constructs, not the items.
  • You want measurement error corrected
    Modelling the latents disattenuates the structural paths in a way path analysis on scale scores cannot.
  • A measurement model plus a structural theory
    e.g. latent job stress → latent burnout → latent performance, each with several indicators.

When NOT to — use instead

  • Only observed variables
    No latent constructs to model — path analysis is the right tool. → Path analysis
  • Prediction with small n or formative constructs
    Covariance-based SEM needs a good sample and reflective indicators. → PLS-SEM
  • You only need to confirm the measurement model
    If there is no structural theory yet, fit the measurement model alone first. → Confirmatory factor analysis

Hypotheses

H₀: the full SEM (measurement + structural) reproduces the observed covariance matrix — exact fit.
Hₐ: the model does not fit. Evaluated by χ² and approximate-fit indices (CFI ≥ .95, RMSEA ≤ .06, SRMR ≤ .08 as common targets), together with the latent-path estimates.

Parameter tested: the structural paths among latent constructs (corrected for measurement error), the measurement loadings, and overall fit indices

Assumptions (and what to do if they fail)

A sound measurement model firsthigh

Check: Each latent should have a well-fitting CFA (loadings, reliability) before the structural paths are interpreted.

If violated: Structural paths among poorly-measured latents are not trustworthy — fix measurement before structure.

Adequate sample sizehigh

Check: SEM is large-sample; rules of thumb ask for many cases per estimated parameter.

If violated: Estimates fail to converge or give improper solutions (negative variances, loadings > 1).

Model identificationhigh

Check: Each latent needs a scale set (a fixed loading or fixed variance) and enough indicators.

If violated: The model is unidentified and the solution is arbitrary.

Multivariate normality (for ML)medium

Check: Default ML assumes it; check skew/kurtosis of indicators.

If violated: Use a robust ML estimator (MLR); otherwise χ² and SEs are biased.

Ready to run a Full SEM (latents + structural) on your own data?

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

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