[R] lmer syntax, matrix of (grouped) covariates?

[Douglas Bates]

On Mon, Aug 18, 2008 at 11:20 AM, Aaron Mackey <ajmackey at gmail.com> wrote:
> I have a fairly large model:

>> length(Y)
> [1] 3051
>> dim(covariates)
> [1] 3051  211

> All of these 211 covariates need to be nested hierarchically within a
> grouping "class", of which there are 8.  I have an accessory vector, "
> cov2class" that specifies the mapping between covariates and the 8 classes.

> Now, I understand I can break all this information up into individual
> vectors (cov1, cov2, ..., cov211, class1, class2, ..., class8), and do
> something like this:

> model <- lmer(Y ~ 1 + cov1 + cov2 + ... + cov211 +
>                  (cov1 + cov2 + ... | class1) +
>                  (...) +
>                  (... + cov210 + cov211 | class8)

> But I'd like keep things syntactically simpler, and use the covariates
> and cov2class
> variables directly.  I haven't been able to find the right syntactic sugar
> to get this done.

Before considering the syntax you should consider the complexity of
the model.  Even with 3000+ observations estimating fixed effects for
over 200 covariates is a risky business.  To follow that up by
incorporating dozens of covariates in a vector-valued random effects
term with a general variance covariance matrix is not likely to be
productive.  When estimating variances and covariances of random
effects the complexity of the estimation problem increases according
to the square of the dimension of each random-effects vector.  For a
term of the form (1|fac) there is one variance-covariance parameter to
estimate.  For a term of the form (1+x|fac) there are 3 such
parameters to estimate, (1+x1+x2|fac) requires 6, etc.  Assuming that
your 211 covariates are more-or-less equally distributed among the 8
classes you would have about 27 per class which means that you have
378 variance-covariance parameters to estimate for each of your 8
classes.  Even with 3000+ observations it would be optimistic to
expect to estimate that many variance-covariance parameters.

You may want to move your question to the R-SIG-Mixed-Models mailing
list and follow up on the model specification there.