[R-sig-ME] Extracting Standard Errors of Uncorrelated Random Effects?

[Douglas Bates]

On Wed, Dec 14, 2011 at 1:05 PM, Derek Dunfield <dunfield at mit.edu> wrote:
> Hello all:
> I was hoping to extract SE for my random effects to get a better idea
> of their precision for each grouping factor.
>
> Andrew Gelman has developed a nice package called "Arm" which does
> this seamlessly for models with correlated random effects such as
> Reaction ~ 1 + Days + (1 + Days | Subject)
>
> When I try to run this on an uncorrelated model such as
> Reaction ~ 1 + Days + (1 | Subject) + (0 + Days | Subject)
>
> I get the error "Error in .local(object, ...) : Code not written yet"

Unfortunately, it is complicated.  Strangely enough, the case of
correlated random effects is easier than the case of uncorrelated
effects.  The values that you want to get are the solutions to a
system like L x = cbind(e_i, e_j) where the indices i and j are the
random effects corresponding to the k'th level of the grouping factor
and L is the sparse Cholesky factor.  For correlated random effects
the i and j are going to be adjacent.  For uncorrelated random effects
they may end up being adjacent after the fill-reducing permutation but
that is not guaranteed.

In this particular case things work out fine.  If I fit that model as
fm1 then I can check that the random effects for each subject are
adjacent by examining

image(fm1 at L)

where we can see that each of the pairs of blocks starting with 1:2
are correlated within the block but orthogonal to the other blocks.
So, setting

L <- fm1 at L
Id <- Diagonal(x = rep.int(1, ncol(L))   # Identity matrix of the same size as L

 the conditional variance-covariance matrix of the orthogonal random
effects for subject 1 is something like

crossprod(solve(L, Id[,1:2], sys="L")) * lme4:::sigma(fm1)^2

Before using such an expression I would check it against the results
from the "Arm" package for the model with correlated random effects.
It is entirely possible that I have left something out of the
calculation.

If you wonder why something that looks simple like this is not part of
the lme4 package, it is because a lot of the simplicity comes from the
fact that both random-effects terms have the same grouping factor.
The general case is much messier.

> I believe this may be due to some unfinished code in the lme4 package
> for ranef, though I'm not sure.
>
> Does anyone have an idea how I could go about calculating these standard errors?
>
> Many thanks in advance for you help!
> :Derek
>
> --
> Derek Dunfield, PhD
> Postdoctoral Fellow, MIT Intelligence Initiative
> Sloan School of Management
> MIT Center for Neuroeconomics, Prelec Lab
> 77 Massachusetts Ave E62-585
> Cambridge MA 02139
>
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