Most researchers new to structural equation modelling open the software and start drawing. Yet in SEM the most critical decisions are made before AMOS is opened at all.

Structural equation modelling with AMOS
In SEM, specifying a model demands theoretical clarity before software skill.

Structural equation modelling (SEM) lets you test relationships among several variables simultaneously while accounting for measurement error. That is its main advantage over regression: it brings the latent structure behind your observed items into the model itself.

But that power carries an obligation. In SEM it is easy to find a model that fits; it is hard to build one that can be defended. The difference lies in the four decisions below.

1. Derive the model from theory, not from the data

SEM is a confirmatory method. Which variable predicts which, and which item loads on which factor, are expected to be settled before the analysis. Looking at the data and keeping whichever path turns out significant is statistically possible but scientifically indefensible.

This is also the objection you will meet most often in peer review: why is this path specified in this direction? If your answer does not rest on a source, the model will be rejected.

2. Test the measurement model before the structural model

The two-step approach is standard practice in SEM. You first test whether your measurement model fits the data using confirmatory factor analysis (CFA), and only once the measurement model shows acceptable fit do you add the structural relationships.

Skip this order and you cannot tell where poor fit comes from: is the problem in your instrument, or in the relationships you specified? The two-step approach removes that ambiguity.

Commonly used fit thresholds

  • χ²/df — below 3 is good, below 5 is generally considered acceptable
  • CFI and TLI — above .95 is good, above .90 acceptable
  • RMSEA — below .06 is good, below .08 acceptable
  • SRMR — below .08

These values derive from Hu and Bentler’s (1999) simulation study. The authors themselves stress that they are not rigid rules but criteria to be interpreted in the light of sample size and model complexity.

3. Use modification indices with care

AMOS will tell you how much fit would improve if you added a given parameter. That information is tempting, and dangerous.

Careful: adding a covariance between error terms on the strength of a modification index almost always improves fit. But if the addition cannot be justified theoretically, what you are doing is fitting the model to the data rather than testing a theory. Such a model is unlikely to replicate in another sample.

The general principle: apply a modification only if you can explain in one sentence why it makes sense. Two items in the same subscale sharing a similar wording structure, for example, is an acceptable justification for an error covariance. “Fit improved” is not a justification.

4. Plan the sample size from the start

There is no single magic number for SEM. The sample you need depends on model complexity, the number of indicators, the strength of the factor loadings and the normality of the data. As a practical starting point, however, targeting 10–20 participants per estimated free parameter is a common approach.

The better route is a power analysis by Monte Carlo simulation before you collect data. It is the strongest answer you can give in peer review to “was the sample adequate?”

In short

  1. Clarify the theoryWhy is each path there? Every arrow should rest on a source.
  2. Test the measurement modelDo not move to the structural model until CFA shows acceptable fit.
  3. Judge fit as a wholeDo not read a single index; χ², CFI, RMSEA and SRMR are read together.
  4. Justify every modificationIf you cannot explain it, do not apply it.
  5. Report transparentlyWrite up the alternative models you tried. Reviewers appreciate it.

SEM with AMOS course

If you would like to learn each of these steps hands-on, working with your own dataset, take a look at our course. Small groups, live and applied.

Course details →

References

  1. Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis. Structural Equation Modeling, 6(1), 1–55.
  2. Kline, R. B. (2023). Principles and practice of structural equation modeling (5th ed.). Guilford Press.