Structural Equation Modeling

Q: Is SEM free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

Q: Do I need to know lavaan syntax?

No. You can describe your model in plain English and StatRyx will translate it. For experienced users, lavaan syntax is fully supported.

Q: What sample size do I need for SEM?

A common rule of thumb is 10–20 observations per free parameter, with an absolute minimum of 100–200. StatRyx will warn you if your sample is too small.

Q: What fit indices does StatRyx report?

StatRyx reports CFI (≥.95 excellent), TLI (≥.95 excellent), RMSEA (≤.06 excellent), SRMR (≤.08 excellent), AIC, and BIC. Chi-square and degrees of freedom are also reported.

Q: How do I report SEM results in APA 7?

Report the estimator, the fit indices (χ² with df and p, CFI, TLI, RMSEA with its 90% CI, SRMR), then the standardised path coefficients with SE and p, ideally in a path diagram. Report the measurement model (loadings, reliability) before the structural model.

Model complex relationships between latent and observed variables — no AMOS, no Mplus, no syntax required.

Structural Equation Modeling (SEM) is a powerful multivariate technique that combines factor analysis and multiple regression. It allows you to model complex relationships between observed variables and latent constructs that cannot be measured directly, such as intelligence, anxiety, or brand loyalty.

SEM simultaneously tests a measurement model (how well observed items represent latent factors) and a structural model (how latent factors relate to each other and to outcomes). It is the standard method for testing mediation in complex multi-construct models and is required in many top-tier journals.

StatRyx implements SEM using the semopy engine, supporting lavaan-style model syntax. Simply write equations like 'Anxiety =~ item1 + item2 + item3' and 'Outcome ~ Anxiety + Control' and StatRyx fits the model, checks convergence, and returns CFI, TLI, RMSEA, SRMR, AIC, BIC, and all standardised path coefficients.

SEM combines a measurement model — how well observed items reflect each latent construct (a confirmatory factor analysis) — with a structural model of the paths between constructs. Evaluate the model in that order: first check that the measurement model fits and the loadings are adequate (above about .50), then interpret the structural paths. Fit is judged from several indices together, typically CFI and TLI ≥ .95, RMSEA ≤ .06 and SRMR ≤ .08 (Hu & Bentler, 1999).

When to use the Structural Equation Modeling

You have latent constructs measured by multiple observed indicators (Confirmatory Factor Analysis)
You want to test a mediation model with multiple mediators simultaneously
You need to test path relationships between multiple constructs in one model
Your research requires fit indices (CFI, RMSEA, SRMR) for model evaluation

When not to use it

You have fewer than ~100–200 observations — use Structural regression or path analysis with observed variables instead
You want exploratory factor analysis (no theory-driven structure) — use Factor Analysis (EFA) instead
You only need a simple mediation test with one mediator — use Mediation Analysis instead

Worked example

Path	Estimate	Std. Error	β	p
Anxiety =~ item1	1.000	—	.72	fixed
Anxiety =~ item2	0.843	0.091	.68	< .001
Anxiety =~ item3	0.911	0.098	.74	< .001
Performance ~ Anxiety	−0.412	0.081	−.41	< .001
Performance ~ Control	0.287	0.069	.29	< .001

How to report it (APA 7)

The structural model showed acceptable fit, χ²(12) = 18.43, p = .10, CFI = .97, TLI = .96, RMSEA = .055 [90% CI: .000, .098], SRMR = .048. The path from Anxiety to Performance was significant (β = −.41, SE = .08, p < .001).

Frequently asked questions

Is SEM free on StatRyx?