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It is postulated that one of the main issue is to find an appropriate covariance structure for repeated measures designs [Ref1]. SAS' PROC MIXED contains a number of covariance structures.

Despite "many choices among models to fit to a given data set in the mixed model setting... [and] we must always remember that all models are wrong (because they are idealized simplifications of Nature), but some are useful [citation]." there are different recommendations for choosing among the covariance models are known [Ref2], [Ref3].

I do experiments with simple one-way within-subjects RM ANOVA (balanced and unbalanced) design without a between-subject factor described here.

My question is
*how is it important if I have a "condition" (not time) as a within-subject factor and how to choose an appropriate covariance structure in this case*?

Perhaps this is a strange case as I have a native substance and its chemical derivatives with similar molecular structures. So probably I have correlation caused by the substance itself?

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    $\begingroup$ Thanks for the references: I had read in Littell et al.'s "SAS for Mixed Models" book that using AIC might be a reasonable way to choose between two covariance structures for otherwise identically specified models $\endgroup$ Commented Mar 21, 2013 at 1:46

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If you have no basis for a particular correlation structure and the unstructured correlation option requires too many parameters, I would try two different ones to see if the results are sensitive to the choice . In my experience they usually aren't sensitive. I would probably compare AR(1) to compound symmetry.

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  • $\begingroup$ thank you for you suggestion. But what characteristics do I have to look at? $\endgroup$
    – abc
    Commented Jun 15, 2012 at 4:04
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    $\begingroup$ You just want to see the extent to which the results change depending on the choice of covariance structure. $\endgroup$ Commented Jun 15, 2012 at 4:18
  • $\begingroup$ OK. And the minimal Akaike Information Criterion is one of them. Right? (as noted by G.E.Dallal "Choosing Among Covariance Structures") $\endgroup$
    – abc
    Commented Jun 15, 2012 at 10:15
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    $\begingroup$ Not exactly. AIC is a criterion to minimize when selecting between models. What I was referring to is really a subjective assessment of the change in fit or the change in the AIC if you want to look at it that way. $\endgroup$ Commented Jun 15, 2012 at 10:37

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