What Is SEM? Structural Equation Modeling, Path Analysis and Latent Variables - A Thesis Guide
What SEM (structural equation modeling) is, path analysis vs latent-variable models, the measurement and structural model, fit indices (CFI, RMSEA, SRMR), sample size, software (AMOS, lavaan) and APA reporting.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
SEM (Structural Equation Modeling) is a family of methods for testing a whole model at once: several variables, several relationships, and sometimes variables that can't be measured directly. If your supervisor said "run SEM" or "do a path analysis", this guide explains what it is, when to use it and what to report.
SEM in one sentence
Regression tests one equation: several predictors → one outcome. SEM tests several equations together, including a variable that is the outcome of one and a predictor in another (a mediator), and compares the whole model with the data: does the picture you drew fit what was measured?
Three concepts to know
Observed variable: something measured directly - a questionnaire item, a score, age.
Latent variable: a concept that isn't measured directly but inferred from several observed variables. "Anxiety" is latent; the ten items of the anxiety questionnaire are its observed indicators. The advantage: SEM corrects for the items' measurement error, so estimates are more accurate than with an item mean.
Path analysis: SEM with observed variables only - e.g. computed scale scores. The simplest form, good for mediation models with several mediators.
The two parts of the model
| Part | What it tests | The question |
|---|---|---|
| Measurement model (CFA - confirmatory factor analysis) | whether the items really measure their latent variables | "Does the questionnaire measure what it should?" |
| Structural model | the relationships between latent variables | "Does anxiety predict performance through worry?" |
The usual order: test the measurement model first; only if it's sound, move to the structural model.
Fit indices: does the model fit the data?
SEM has no single p-value. You read several fit indices together. Common rules of thumb (Hu & Bentler, 1999):
| Index | Good fit |
|---|---|
| χ² | non-significant - but almost always significant in large samples, so not used alone |
| CFI / TLI | .95 or above (.90 acceptable) |
| RMSEA | .06 or below (up to .08 acceptable), with its confidence interval |
| SRMR | .08 or below |
These are rules of thumb, not laws: report several indices and interpret them together.
How many participants?
There's no single rule, but SEM is data-hungry. A common rule of thumb is 200+ for moderately sized latent models; a simple path analysis can manage with fewer. A complex model with a small sample gives unstable estimates or fails to converge. See Sample size and power.
Which software?
- AMOS (SPSS add-on) - draw the model graphically. Common at Israeli universities.
- lavaan (free R package) - write the model in a few lines of code; very flexible.
- Mplus - especially strong for complex models; paid.
- JASP (free) - an SEM module built on lavaan, with a simple interface.
Reporting in APA
Report the measurement model, the fit indices and the standardised path coefficients - usually in a diagram with coefficients on the arrows:
"The measurement model fit the data well, χ²(48) = 71.32, p = .016, CFI = .97, TLI = .96, RMSEA = .048, 90% CI [.022, .070], SRMR = .041. In the structural model, test anxiety predicted worry (β = .58, p < .001), and worry predicted lower performance (β = −.34, p < .001). The indirect effect was significant, β = −.20, 95% CI [−.29, −.12]."
SEM or PROCESS?
With one mediator or moderator and scale scores, PROCESS in SPSS is simpler and enough. Move to SEM with chains of mediators, several outcomes, latent variables, or when your supervisor wants the questionnaire's structure tested (CFA).
Common mistakes
- Reporting only χ² - or rejecting a model just because χ² is significant in a large sample.
- Modifying the model by "Modification Indices" without theoretical justification - that fits the model to the data instead of testing it.
- Skipping the measurement model.
- Reading SEM as proof of causation - other models may fit just as well.
- A sample too small for the model's complexity.
FAQ
What's the difference between SEM and regression? Regression is one equation with observed variables. SEM tests several equations together, can include latent variables, and gives indices of how well the whole model fits.
What is a latent variable? A concept not measured directly but inferred from several items - like anxiety, motivation or intelligence.
Path analysis vs SEM? Path analysis is SEM with observed variables only, no latent variables.
What is a good RMSEA? .06 or below is good fit, up to .08 acceptable. Report its confidence interval too.
My supervisor asked for SEM and I don't know where to start. That's exactly the kind of analysis we guide. Tell us about your model and we'll go through every step, from the diagram to the write-up.
Source
- Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55.
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