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I’m looking into SEM (Structural equation modelling using covariance matrixes) as an analysis technique and am finding it difficult to find consistent information on the assumptions of the technique. Below is what I currently have from reviewing the literature over the last couple of days. Is this a complete list to check before undertaking SEM? If not, could anyone point me in the direction of assumptions I may have missed or correct me on my current ones?

  1. Common Method Bias
  2. Outliers
  3. Multicollinearity
  4. Multivariate Normality
  5. Relationship between the observed variables and their constructs and between one construct and another is linear.
  6. No Missing Data
  7. Unidimensionality Of Constructs
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There's nothing special or magically different about structural equation modeling (SEM) and other statistical techniques. Regression (and hence t-tests, anova), manova, etc can all be thought of as special cases of structural equation models. In addition, SEM and multilevel models are often equivalent - see http://curran.web.unc.edu/files/2015/03/Curran2003.pdf [edit: link updated, thanks @Peter Humburg) . If something is an assumption in statistical analysis generally, it's an assumption in SEM. If something is an issue or a problem in statistical analysis generally, it's an issue or a problem in SEM.

  1. Common method bias is an issue in the interpretation of your model. It's not an assumption.
  2. Think of multiple regression as being a structural equation model. If it's an assumption in regression, it's an assumption in SEM. Outliers are a problem in regression, and a problem in SEM.
  3. Multicollinearity is not an assumption in regression, or SEM, unless your matrices cannot be inverted because they are not positive definite, in which case it's an assumption everyone. It's a problem.
  4. Normality is an assumption in regular ML, as it is in regular OLS regression. But there are ways to handle it (as there are in regression).
  5. Linearity is as assumption, there are ways around it but they vary from "a bit fiddly" to "really hard".
  6. There are ways to handle data that are missing at random or missing completely at random, same as (almost) every other type of statistical analysis. It's a problem, and the solutions bring assumptions.
  7. Not an assumption, it's something that your model can test.
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  • $\begingroup$ The link is dead. The paywalled version of that article is available here. $\endgroup$ – Peter Humburg Jun 5 at 5:57
  • $\begingroup$ Thanks. Link updated to non-paywalled version. $\endgroup$ – Jeremy Miles Jun 6 at 0:38

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