[R] type I and type III sums of squares

[Paul Litvak]

Hello-

I have been digging around in the FAQ's and online looking for an answer 
to my questions, and perhaps someone here can help me.

For a statistical experiment, I need to run 3,000,000 ANOVAs, which is 
taking me a very long time. As a result, I have recoded my analyses in 
C. However, I cannot find the formula to calculate either the type I or 
type III sums of squares (in the case of my model, the two are 
equivalent). I know that the formula must be in the R source code, as 
they are able to calculate it, but I am not sure where. Does anyone know 
where I can find the explicit procedure for calculating this? A 
mathematical formula or the source code would be equally helpful. I am 
aware of the formula in matrix algebra, but is there a formulation that 
does not use matrix algebra?

thanks very much in advance,
Paul Litvak
Department of Human Genetics
University of Michigan