negative values in compound symmetry covariance structure

[Peter_Y]

Hello:

  I have two questions about the covariance structure in proc mixed.

1. I realize the compound symmetry structure allows the covariance term to be negative.  This is different from the literature where the covaraince is always positive so it is equivalent to a random intercept model. Why SAS define it differently? I can hardly imagine a situation where the repeated measure are mutually negative correlated. Is this even possible?
2. I don't understand the default variance components structure. see SAS/STAT(R) 9.2 User's Guide, Second Edition.  Why the first two variances equal to sigma^2_B and the second two equal to sigma^2_AB. What do the subscript B and AB represent?

Thanks,

Peter

[lvm]

For 1, it is actually fairly common for the covariance to be negative. I get this result a lot for some data structures and models. You are not correct that "the covariance is always positive". If subject is a block, then a negative covariance means that two randomly chosen observations within the same block are negatively correlated (or that there is more variation within blocks than between blocks). And for repeated measures, it is definitely possible for observations within a subject to have a negative correlation.

Can't answer your second question because the link is too general. Not clear what part you are asking about. But B is generic for main effect B (random effect) and AB is the interaction of A (presumed fixed) and B.

I highly recommend that you get a copy of SAS for Mixed Models, second edition (2006; SAS, Inc.), by Littell et al.