Some things you only discover after the data are in: that the structural model you designed cannot be estimated at all, or that the sample was never large enough for the path coefficients to reach significance.
Both are checkable before collection begins. What the calculation needs is the structure of the model and an expected effect size, not responses.
This article covers how to check identification, what actually determines sample size, and how to prepare mediation and moderation hypotheses at the planning stage.
Model Identification — A Model That Will Not Run Is Not a Data Problem
When an estimator fails to converge or returns something impossible like a negative variance, the instinct is to suspect the data. Often the model simply is not identified.
Identification compares the information the data provide against the number of parameters to be estimated. With p observed variables, the covariance matrix supplies p(p+1)/2 pieces of information. If the model asks for more parameters than that, infinitely many solutions exist and estimation cannot proceed. The requirement that degrees of freedom be zero or greater comes from this.
That condition is necessary but not sufficient. A model can carry spare degrees of freedom and still fail because some part of it is locally unidentified. A factor with only two indicators is the classic case: it estimates when correlated with another factor, but unstably, and it is not identified in isolation. The convention of three or more indicators per factor comes from this.
Setting the scale of each latent variable is also part of identification. Either fix the first loading to 1 or fix the factor variance to 1; one of the two is required.
What Actually Determines Sample Size
"Is 200 enough?" cannot be answered without seeing the model. The same 200 respondents mean very different things for a model estimating 30 parameters and one estimating 90.
| Criterion | Content | Nature |
|---|---|---|
| N ≥ 200 | Conventional minimum | Rule of thumb |
| N : q ≥ 10 | Cases to estimated parameters | Rule of thumb |
| RMSEA-based power | Required N for a target power level | Statistical determination |
The first two are conventions documented in Kline (2015). They are useful for a quick read but rest on practice rather than calculation. When a journal asks you to justify your sample size, the third is what answers it.
The RMSEA-based power analysis proposed by MacCallum, Browne & Sugawara (1996) takes a null and alternative RMSEA value, the degrees of freedom, and a target power level, and returns the required sample size. One result runs against intuition: models with more degrees of freedom need smaller samples for the same power, because a more constrained model offers more opportunities to detect misfit.
Can G*Power Determine SEM Sample Size?
No. G*Power covers power for t tests, ANOVA, and regression, and it does not handle the model fit test in structural equation modeling. Reporting a number from its regression module, with the number of predictors entered, as an SEM sample size justification is common and unfounded, because that calculation ignores measurement error in latent variables.
For SEM, use the RMSEA-based determination, or run a Monte Carlo simulation when the model is complex or when conditions like missingness and non-normality need to be reflected. The simulation approach generates data repeatedly from assumed parameter values and counts how often the effect reaches significance, which suits mediation in particular, where the sampling distribution is skewed.
Test Mediation With Bootstrapping, Not the Sobel Test
Manuscripts still appear using the Sobel test for indirect effects. That test assumes the sampling distribution of the indirect effect is normal, while the product of two coefficients is generally skewed. The smaller the sample, the worse the distortion.
The bootstrapping approach set out in Preacher & Hayes (2008) is the standard. Resampling with replacement builds an empirical distribution of the indirect effect and yields a confidence interval; if that interval excludes zero, the effect is treated as significant. Five thousand resamples or more is typical.
What matters at the planning stage is not the method but the power. An indirect effect is the product of two paths, so even two moderate paths multiply into something small. A sample that comfortably detects a direct effect is often short for the indirect one.
Moderation Needs a Larger Sample, Planned in Advance
Interaction terms carry less power than main effects. Measurement error enters from both constituent variables, so the interaction term is less reliable than either of them. Moderation failing to reach significance in a sample where main effects are clean is a routine outcome.
If moderation is the central hypothesis, size the sample against that hypothesis rather than the main effects. If you plan to test moderation by splitting groups and running multi-group analysis, add the condition that each group must be large enough to estimate on its own.
What modidoc Does at the Structural Pre-Check Stage
modidoc's structural pre-check stage computes the degrees of freedom and identification conditions of the model you designed and reports whether it is estimable before anything else, then derives the sample size required for your target power given that model structure. When mediation or moderation hypotheses are included, it reports the sample requirement implied by those hypotheses as well. This stage is implemented internally as the C8 structural pre-check engine.
Frequently Asked Questions
What does model identification mean in SEM?
Whether the information in the data allows the model's parameters to be estimated uniquely. With p observed variables the data supply p(p+1)/2 pieces of information, and a model asking for more parameters than that has no determinate solution. Degrees of freedom of zero or more is the necessary condition; a model can still fail when part of it is locally unidentified, as with a factor carrying only two indicators.
How do I calculate sample size with G*Power?
For regression or ANOVA, enter the effect size, alpha, target power, and number of predictors. It does not apply to structural equation modeling. SEM requires RMSEA-based power analysis (MacCallum, Browne & Sugawara, 1996) or Monte Carlo simulation, and presenting a G*Power figure as an SEM sample size justification is something reviewers flag.
What is bootstrapping for mediation?
Resampling with replacement to build an empirical distribution of the indirect effect and taking a confidence interval from that distribution. If the interval excludes zero, the indirect effect is treated as significant. Unlike the Sobel test it assumes no normality, which fits the skewed distribution formed by the product of two coefficients. Reporting 5,000 or more resamples with bias-corrected intervals is the convention (Preacher & Hayes, 2008).
The next article covers the final checks before a finished questionnaire goes out: how item order affects responses, handling reverse-coded items, and what belongs in a codebook.
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