Statistical Associates Publishers

## Structural Equation Modeling: 10 Worst Pitfalls and Mistakes

1. Not testing the measurement model.
There is no point in testing the structural model until the measurement model is upheld.

2. Testing only one model
For any given set of data it is possible more than one model will have "good fit". It is better to compare models to determine which has better fit.

3. Thinking good fit is a strong model.
Good fit only means the model conforms to the covariance matrix presented by the data. Even the independence model will have good fit if variables are uncorrelated.

4. Violating linearity.
The right-hand predictor side of the equation must be linear with the left-hand outcome side of the equation. Most SEM models use linear regression. Even if generalized SEM is used, the researcher must test for linearity in the transform (ex., in logistic regression test for linearity in the logit, which is the transformed outcome).

5. Treating ordinal data as interval in level.
This is the same violation as is common in multiple linear regression. There are various approaches to the use of ordinal data in SEM, such as Bayesian SEM, generalized SEM, and use of polychoric correlation matrix input.

6. Reporting results in spite of a warning that the covariance matrix is not positive definite or if convergence is not achieved.
Although statistical programs may generate output, goodness of fit measures may be inaccurate, even extremely inaccurate, if the covariance matrix is not positive definite or for other reasons convergence is not achieved.

7. Using SEM with small samples .
SEM typically uses maximum likelihood estimation, which requires a larger sample size than the corresponding OLS regression. SEM analyses are typically for samples of 200 or greater.

8. Using modification indexes atheoretically .
Modification index (MI) and Lagrange multiplier (LM) coefficients flag possible opportunities to add arrows to the model to achieve better fit. However, to do so on a data-driven basis without a theoretical justification for each added arrow is a mistake.

9. Using significance tests when you do not have a random sample. .
If you have a random sample, you can generalize to the population from which it is drawn if a path coefficient is significant. If you have an enumeration (all the cases in the population to which you wish to generalize), significance testing is irrelevant. If you have a non-random sample, significance tests will be in error to an unknown degree. No, bootstrapped significance tests will not solve this problem of inability to generalize, though they do help when the sample is random but the distribution is non-normal or unknown.

10. Not meeting the assumptions of multiple linear regression in ordinary SEM, or the assumptions of other types of regression in generalized SEM. .
Our book, listed below, enumerates many assumptions of SEM, clearly listed in the "Assumptions" section.