[R] Fitting mixed-effects models with lme with fixed error term variances

[Gregor Gorjanc]

Douglas Bates wrote:
> On 11/21/06, Gregor Gorjanc <gregor.gorjanc at bfro.uni-lj.si> wrote:
>> Douglas Bates <bates <at> stat.wisc.edu> writes:
>> ...>
>> > Can you be more specific about which parameters you want to fix and
>> > which you want to vary in the optimization?
>>
>> It would be nice to have the ability to fix all variances i.e.
>> variances of
>> random effects.
> 
> That gets tricky in terms of the parameterization of the
> variance-covariance matrices for vector-valued random effects.  These
> matrices are not expressed in the conventional parameterization of
> variances and covariances or even variances and correlation because
> the conditions for the resulting matrix to be positive definite are
> not simple bounds or easily expressed transformations then the matrix
> is larger than 2 by 2.  I suppose what I could do is to allow these
> matrices to be specified in the parameterization that is used in the
> optimization and provide a utility function to map from the
> conventional parameters to these.  That would mean that you couldn't
> fix ,say, the variance of the intercept term for vector-valued random
> effects but allow the variance of a slope for the same grouping factor
> to be estimated.  Well, you could but only in the fortune("Yoda")
> sense.
> 

Yes, I agree here. Thank you for the detailed answer.

> By the way, if you fix all the variances then what are you optimizing
> over?  The fixed effects?  In that case the solution can be calculated
> explicitly for a linear mixed model.  The conditional estimates of the
> fixed effects given the variance components are the solution to a
> penalized linear least squares problem.  (Yes, the solution can also
> be expressed as a generalized linear least squares problem but there
> are advantages to using the penalized least squares representation.

Yup. It would really be great to be able to do that nicely in R, say use
lmer() once and since this might take some time use estimates of
variance components next time to get fixed and random effects. Is this
possible with lmer or any related function - not in fortune("Yoda") sense ;)

-- 
Lep pozdrav / With regards,
    Gregor Gorjanc
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University of Ljubljana     PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
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