[R] unbalanced design for anova with low number of replicates

[Liaw, Andy]

Arne,

For this sort of things, my suggestion is that you try to seek assistance
from local statistician(s), and I'd be very surprised if there's none for
you.

Data arising from unbalanced designs need no special tools for model
fitting.  The garden variety linear models work just fine.  The problem is
what do you do with the model(s):  The inference is where the problem is.
Unbalanced design introduce (partial) confounding among factors, which makes
assessment of effects tricky.  It really depends on what your goal is.  As
long as you can formulate that in terms of parameters in the `fullest' model
you are willing to consider, then it just comes down to testing specific
(general) linear hypotheses, which can be done `by hand'.  (I believe Greg
also has a glh() or something like that in the gregmisc package.  I'd guess
Prof. Fox's `car' package also has something similar.)

[BTW, if you are going to treat `batch' as a random effect, you might want
to look into mixed effect models; i.e., lme() in either lme4 or nlme.]

Best,
Andy

> From: Arne.Muller at aventis.com
> 
> Hello,
> 
> I'm wondering what's the best way to analyse an unbalanced 
> design with a low number of replicates. I'm not a 
> statistician, and I'm looking for some direction for this problem.
> 
> I've a 2 factor design:
> 
> Factor batch with 3 levels, and factor dose within each batch 
> with 5 levels. Dose level 1 in batch one is replicated 4 
> times, level 3 is replicated only 2 times. all other levels 
> are replicated 3 times, except for batch level 3, for which 
> dose 4 is missing. 
> 
> I've realised that the other of the factors is critical for 
> the outcome of the anova (using lm and anova).
> 
> I guess the impact wouldn't be strong if there was a 
> reasonably large numbe rof replicates within each cell (even 
> though not balanced). However, since I've only 0 to 4 
> replicates I'm worried that the standard anova may not be the 
> way to go.
> 
> Are there special packages for unbalanced designs like this?
> 
> 	kind regards,
> 
> 	Arne
> 
> --
> Arne Muller, Ph.D.
> Toxicogenomics, Aventis Pharma
> arne dot muller domain=aventis com
> 
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