[R-sig-ME] Is there any chance of development ofmultivariate linear mixed models for lme4

[Douglas Bates]

The way that I would like to approach this kind of model is to
incorporate the variance-covariance of the multivariate response as a
"pre-whitening" transformation.  In the "Implemenentation" vignette in
the lme4 package I describe the representation of a positive
semi-definite matrix (i.e. a general variance-covariance matrix) as
the product of a diagonal matrix and a unit lower-triangular matrix.
That parameterization could be used for the variance-covariance of the
multivariate response.  (It may be necessary to constrain one of the
diagonal elements of the diagonal matrix to 1 because of the profiling
out of the scalar variance parameter.)

Conditional on those parameters the model matrices and responses could
be "pre-whitened" to a set of independent, constant-variance response
and the corresponding model matrices.  These would then update the
ZXyt slot in the mer2 representation and the optimization could
proceed from there.  In lme we used a "nested" optimization.  I think
I would not recommend doing that here.  I would try to do the
optimization jointly.

I imagine there would need to be another factor in the deviance that
takes into account the variance-covariance structure of the responses.

Generally I would like to regard the what I am now calling the mer2
representation (it will become the mer class later when I have all the
necessary methods programmed) as a building block for models that
extend the univariate linear mixed effects model.  These include the
generalized linear mixed effects model, the nonlinear mixed effects
model, the multivariate linear mixed effects model, ...

On 2/2/07, Doran, Harold <HDoran at air.org> wrote:
> I'm interested in seeing this as well. I too have a paper showing how to
> estimate multivariate mixed models. But, I think it is necessary to
> construct a patterned covariance matrix for the residual error and this
> is not available in lmer.
>
> @article{dora:lock:2006,
> year                    ={2006},
> author          ={Harold C. Doran and J.R. Lockwood},
> title                   ={Fitting value-added models in {R}},
> volume          ={31}.
> number          ={2},
> journal         ={Journal of Educational and Behavioral Statistics}
> }
>
> > -----Original Message-----
> > From: r-sig-mixed-models-bounces at r-project.org
> > [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf
> > Of Andrew Robinson
> > Sent: Thursday, February 01, 2007 6:31 PM
> > To: Ian Dworkin
> > Cc: r-sig-mixed-models at r-project.org
> > Subject: Re: [R-sig-ME] Is there any chance of development
> > ofmultivariate linear mixed models for lme4
> >
> > Hi Ian,
> >
> > I've been able to trick lme() into fitting multivariate
> > mixed-effects models, and I don't think that I relied on any
> > functionality that is not available within lmer at the
> > present.  I can send you what I did if you're interested.  I
> > wrote it up in:
> >
> > Robinson, A.P., 2004. Preserving correlation while modelling diameter
> >   distributions. Canadian Journal of Forest Research 34, 221--232.
> >
> > Mind you, the code was ugly and not terribly intuitive!
> >
> > Cheers
> >
> > Andrew
> >
> > On Thu, Feb 01, 2007 at 05:59:54PM -0500, Ian Dworkin wrote:
> > > Hi,
> > >
> > >   From what I gather this is a list primarily dedicated to the
> > > development of mixed model libraries for R. So I apologize
> > if this is
> > > not the appropriate place for this.
> > >
> > >   I am in the process of making the transition from SAS to
> > R. One of
> > > the major procedures I use(d) in SAS was PROC MIXED, and I
> > am slowly
> > > getting familiar with lmer.
> > >
> > >  I was wondering if there is any discussion of working on the
> > > development of multivariate mixed models? Most of the data I am
> > > interested with is multivariate in nature, and univariate
> > methods tend
> > > to be less useful. Not that PROC MIXED does this very
> > effectively, but
> > > you can trick MIXED to do some multivariate models using
> > the repeated
> > > statement and specifying an unstructured covariance matrix etc..
> > > However the code is ugly and not very intuitive.
> > >
> > >   Anyways, I am asking in the vain hope that something is being
> > > developed in lme4 for multivariate models.
> > >
> > > Thanks
> > >
> > > Ian
> > >
> > > _______________________________________________
> > > R-sig-mixed-models at r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> > --
> > Andrew Robinson
> > Department of Mathematics and Statistics            Tel:
> > +61-3-8344-9763
> > University of Melbourne, VIC 3010 Australia         Fax:
> > +61-3-8344-4599
> > http://www.ms.unimelb.edu.au/~andrewpr
> > http://blogs.mbs.edu/fishing-in-the-bay/
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
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