How do you know if the covariance structure you select for your random effects in a mixed model is the best one? There are many different types of covariance structures to choose from. How do you assess what the best structure is? For example, if I am choosing between unstructured vs. compound symmetry. Is there a certain test I need to run when I run the model in SAS or R?
 A: A couple of points:


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*To select the appropriate covariance structure for your data, it is advisable to have an adequate specification of your mean structure. This means including even terms that you may not need (e.g., interaction or nonlinear terms).

*There are indeed many different covariance structures available in various software. Before going into statistically selecting which one is appropriate for your data, it would be a good idea to restrict the options to covariance structures that are plausible/relevant for your design. For example, if you have longitudinal data, typically, you expect that correlations decay with the time lag. If you have a multilevel design, e.g., students nested in classes, and classes nested in schools, then you would typically start with a generalization of the compound symmetry structure.

*The tools to use for selecting between competing covariance structures for your data depend on whether these structures are nested or non-nested. When nested, you can use a likelihood ratio test to get an indication on which fits the data better. Because many times you also have missing data, I typically recommend favoring a more complex structure than a more parsimonious one. Hence, using a higher significance level than the typical 5%. When you have non-nested structures you could use the AIC.

