[R-sig-ME] Doubt about scaling random effects

[Douglas Bates]

Usually it is best to send questions like this to the
R-SIG-Mixed-Models at R-Project.org mailing list (see

https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

for details).  Several of those who read that list can reply to such
questions, often much more quickly than I am able to.

I have taken the liberty of cc:ing that list on this reply.

Having said that, the distinction between the random effects on the
original scale (i.e. the default for ranef) and the "spherical" random
effects used internally is a computational convenience as described in the
paper

https://www.jstatsoft.org/article/view/v067i01

By rephrasing what are sometimes called the mixed-model equations in terms
of the spherical random effects the profiled log-likelihood for a linear
mixed-model can be determined directly from the solution to a penalized
least squares problem.  For a GLMM the step involves a penalized
iteratively reweighted least squares (PIRLS) solution.

In fact, there is a slightly more compact representation and solution than
is provided in that paper as described in

http://dmbates.github.io/MixedModels.jl/latest/optimization.html#Details-of-the-parameter-estimation-1

and implemented in the MixedModels package for Julia.

On Mon, Nov 27, 2017 at 2:30 PM Sofia Pignataro <sofia.pignataro at gmail.com>
wrote:

> Dear PhD Bates,
>
> I am using a GLMM Poisson through glmer function from lme4 package. I
> would like to know the difference between scaled/standardized random
> effects (default in ranef for GLMM) and random effects that are available
> in the fit object (returned by glmer).
>
> Can you help me or send me a reference where I can find the answer?
>
> Best regards,
> Sofia
>

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