[R-sig-ME] LMM covariance structure

[Douglas Bates]

On Wed, Mar 4, 2009 at 11:15 PM, Pietro Ravani <pravani at ucalgary.ca> wrote:
> I need confirmation or correction on this: how can the structure of
> the R vcv matrix of a LMM have non negative covariances if the
> residuals are independent given the random effects (and the co-
> variates)?

Could you be more explicit about what you mean by "the R vcv matrix of
a LMM" and why you are specifically interested in non-negative?  (Or
did you intend "non-zero"?)  In particular, does "R" in your question
refer to a model fit by R packages such as lme4 or nlme or are you
referring to a conditional variance-covariance structure of the
response given the random effects, which is sometimes written as R?

> Covariance structures such as compound symmetry, AR 1,
> Toeplitz are specified by the user or are the marginal type of vcv
> implied/induced by the random effects?