[R-sig-ME] Mixed-models and condition number

[Douglas Bates]

On Mon, Feb 2, 2009 at 11:00 AM, Christina Bogner
<christina.bogner at uni-bayreuth.de> wrote:
> Dear list members,

> I'm working with both nlme and lme4 packages trying to fit linear
> mixed-models to soil chemical and physical data. I know that for linear
> models one can calculate the condition number kappa of the model matrix to
> know whether the problem is well- or ill-conditioned. Does it make any sense
> to compute kappa on the design matrix of the fixed-effects in nlme or lme4?
> For comparison I fitted a simple linear model to my data and scaling some
> numerical predictors decreased kappa considerably. So I wonder if scaling
> them in the mixed-model has any advantages?

I'm not sure that checking the conditioning of only the fixed-effects
model matrix is what you want to do.  In some ways it would be more
informative to check the conditioning of the triangular matrix derived
from the fixed-effects model matrix after removing the random effects.
 That upper triangular matrix is stored as the RX slot.  Generally I
don't recommend reaching in to a structure or an S4 object and pulling
out a piece of it (because you can't count on those slots continuing
to be there and to have the same names and contents) but in this case
it may be the best way of going about things.

If this is considered useful I could add a kappa method for the class.