How to choose an appropriate covariance structure for a simple one-way within-subjects RM ANOVA design?

Question

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?

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 — James Stanley, Mar 21 '13 at 01:46

Michael R. Chernick · Answer 1 · 2012-05-27T23:59:39.487

2

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.

edited May 27 '12 at 23:59

answered May 27 '12 at 14:14

Michael R. Chernick

42,857

thank you for you suggestion. But what characteristics do I have to look at? – abc Jun 15 '12 at 04:04
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You just want to see the extent to which the results change depending on the choice of covariance structure. – Michael R. Chernick Jun 15 '12 at 04:18
OK. And the minimal Akaike Information Criterion is one of them. Right? (as noted by G.E.Dallal "Choosing Among Covariance Structures") – abc Jun 15 '12 at 10:15
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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. – Michael R. Chernick Jun 15 '12 at 10:37

How to choose an appropriate covariance structure for a simple one-way within-subjects RM ANOVA design?

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