Unbalanced Anova: What is the best approach?

I have a three-way unbalanced ANOVA that I need to calculate (fixed effects
plus interactions, no random effects). But word has it that aov() is good
only for balanced designs. I have seen a number of different recommendations
for working with unbalanced designs, but they seem to differ widely (car,
nlme, lme4, etc.). So I would like to know what is the best or most usual
way to go about working with unbalanced designs and extracting a reliable
ANOVA table from them in R?

Actually, without random effects, aov() is not too crazy, but you might as well use plain lm(). In both cases, the main point is that you need to be aware that there is no such thing as "the" ANOVA table: Sums of squares will depend on the order of testing, and there is nothing to do about that (except getting balanced data).

Pragmatically, I'd test the three-factor interaction, then use drop1() on a model with two-factor interactions, if nothing glaringly obvious pops up, try reduction to additive model and then use drop1() again. Obviously, if significant interactions appear, you cannot just remove them and need to investigate what they mean.

Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com