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

Christina Bogner christina.bogner at uni-bayreuth.de
Thu Feb 5 09:21:51 CET 2009

Dear Douglas Bates,

Thank you for your response. I would appreciate if you could add a 
kappa-method to the lme4 package, please. It was indeed rather revealing 
to play around with different design matrices (mean-centered, scaled and 
different reference levels for factors).


Douglas Bates schrieb:
> 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.

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