Contrasts for imbalanced and partially crossed designs

[tavareshugo]

I wonder if the strategy I'm using in the tutorial is actually suitable for imbalanced designs. For example, let's say I had 3 replicates in one batch and 6 replicates in a another batch and am creating a coefficient vector for two treatments. Why should estimates for samples in batch 2 have twice the weight as those from batch 1? In principle the SE estimates already implicitly capture differences in the uncertainty of coefficient estimates in each batch.

There might be situations where it's reasonable to assume different weights, but maybe in most cases we actually want to keep equal weights. Investigate this with simulations.

I've got a getNumericCoef() function in this gist, which I think does the trick.

[tavareshugo]

I'm not entirely sure of the argument above regarding imbalanced designs.

Perhaps more seriously, I'm not confident the approach in the tutorial holds for partially crossed designs - in fact, it may give wrong coefficient weights! See #9 for an example.