Query lme4

Dear Douglas Bates,

I am a research student at Queen's University, Belfast and I am currently
researching methods to analyse longitudinal data through the use of mixed
models. I am interested in using the R package lme4. The syntax I am using
to fit my model is the following,

model.1<-lmer(eGFR_IDMS~AGEACTUAL+(AGEACTUAL|Individual),data=sample,REML=FALSE)

I was wondering would you be able to tell me what covariance structure this
package uses when it models the random effects using the above syntax and if
it is possible to use a compound symmetry and autoregressive covariance
structure to model the random effects through this package. Any help you
could give me would be much appreciated.

The phrase "covariance structure" can mean different things in the
context of mixed models.  The covariance structure of the random
effects for such a model is a block-diagonal matrix of size 2N x 2N
where N is the number of individuals.  There are N diagonal blocks,
each of which is a copy of the 2 x 2 matrix that is returned by
VarCorr(model.1).

Since you mention an autoregressive structure I assume you are
considering the marginal covariance structure of the response vector.
To evaluate that you need to know the model matrix for the random
effects.  The within individual covariance structure is of the form

Z_i %*% D %*% Z_i' + sigma^2 I

where Z_i is the two-column model matrix for the i'th individual and D
is the 2 x 2 variance-covariance matrix returned by VarCorr(model.1),
sigma is the residual standard error and I is the n_i x n_i identity
matrix.

The marginal variance-covariance matrix for the model with random
effects specification (1|individual) has a compound symmetry
structure.

The lme4 package does not have capabilities of modeling an
autoregressive structure.  In most cases of longitudinal data it would
be very difficult to distinguish between an autoregressive structure
and a model with random effects specification (AGEACTUAL|Individual).

I have taken the liberty of copying the
R-SIG-mixed-models at R-project.org mailing list on this reply.  It is
usually more effective to send such queries to that list rather than
to me personally as sometimes I take a while to respond.

Kind Regards,

Lisa McCrink