[R] Two-way Random Effects with unbalanced data

asafwe asafw at wharton.upenn.edu
Mon Oct 29 22:42:37 CET 2012

Hi there,

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

                              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,


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