R help - Oct 2012 - Two-way Random Effects with unbalanced data

Hi there,

I am looking to fit a two-way random effects model to an *unblalanced*
layout,

                              y_ijk = mu + a_i + b_j + eps_ijk,    
i=1,...,R, j=1,...,C, k=1,...,K_ij.

I am interested first of all in estimates for the variance components,
sigsq_a,  sigsq_b and sigsq_error.
In the balanced case, there are simple (MM, MLE) estimates for these; In the
unbalanced setup, this is much more complicated because orthogonality
relations no longer exist between "row space" and "column
space". Since the
covariance structure between the cell means y_{ij.} is much more complicated
than in the one-way (unbalanced) case, trying to manually obtain MLEs looks
very difficult.
I couldn't find anything addressing point estimates for the unbalanced case
- neither in the literature nor in a computer program (R or alike). 

Any idea will be greatly appreciated...

Thank you,

Asaf



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Asaf,

I think that the lme4-package on CRAN with its main function lmer() can
help you here. It uses restricted ML to find the estimates and should cope
with unbalanced data. The two factors of your random effects can be either
nested or crossed.
Have a look in the book (draft-version) on lme4 by Doug Bates, in
particular chapter 2.
http://lme4.r-forge.r-project.org/lMMwR/ There is a PDF in that directory.

By the way, there is another mailing list dedicated to mixed-models in R,
the R-sig-mixed-models. You have better chances to get quicker reply in
case you have further questions on lme4..

Matthias.


On Mon, Oct 29, 2012 at 10:42 PM, asafwe <asafw@wharton.upenn.edu> wrote:
> Hi there,
>
> I am looking to fit a two-way random effects model to an *unblalanced*
> layout,
>
>                               y_ijk = mu + a_i + b_j + eps_ijk,
> i=1,...,R, j=1,...,C, k=1,...,K_ij.
>
> I am interested first of all in estimates for the variance components,
> sigsq_a,  sigsq_b and sigsq_error.
> In the balanced case, there are simple (MM, MLE) estimates for these; In
> the
> unbalanced setup, this is much more complicated because orthogonality
> relations no longer exist between "row space" and "column
space". Since the
> covariance structure between the cell means y_{ij.} is much more
> complicated
> than in the one-way (unbalanced) case, trying to manually obtain MLEs looks
> very difficult.
> I couldn't find anything addressing point estimates for the unbalanced
case
> - neither in the literature nor in a computer program (R or alike).
>
> Any idea will be greatly appreciated...
>
> Thank you,
>
> Asaf
>
>
>
> --
> View this message in context:
>
http://r.789695.n4.nabble.com/Two-way-Random-Effects-with-unbalanced-data-tp4647795.html
> Sent from the R help mailing list archive at Nabble.com.
>
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> R-help@r-project.org mailing list
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
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Matthias,

This is so very helpful! 
Thank you so much for exposing me to this. Seems like exactly what I was
looking for.

Best regards,

Asaf



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