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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