Hi Gordon,

In a previous email on the list you said:
> testing for the 2-way interaction in the presence of a 3-way 
> interaction does not make statistical sense.  This is because the 
> parametrization of the 2-way interaction as a subset of the 3-way is 
> somewhat arbitrary.  Before you can test the 2-way interaction 
> species*treatment in a meaningful way you would need to accept that 
> the 3-way interaction is not necessary and remove it from the model.
Does this mean that it is impossible to test for a 2-way interaction 
when your model includes a 3-way interaction term? Or does it just mean 
that the parametrization provided by 
"model.matrix(~1+factor1*factor2*factor3)" is such that the 2-way 
interaction is not represented by any coefficient, but rather by a 
complex contrast?
> I prefer to fit the saturated model (a different level for each 
> treatment combination) and make specific contrasts. There is some 
> discussion of this in the limma User's Guide.
If I understand correctly here, you are saying that one can fit a model 
where each coefficient represents the abundance for one specific 
combination of the 3 factors, as in the Limma User's Guide section 8.5.2 
"Analysing as for a Single Factor". In other words, one could do 
"model.matrix(~0+factor1:factor2:factor3)" and this would be an 
alternate parametrization of the same design. And with this 
parametrization, all the 2- and 3-way interaction terms (and simple 
pairwise comparisons) can easily be tested from the single full 3-way 
interaction by specifying the appropriate contrasts. Do I understand 
correctly?

-Ryan Thompson

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