Re: GLM and interactions

[Jason Stover]

On Sat, Jul 09, 2011 at 08:13:55AM +0000, John Darrington wrote:
> On Fri, Jul 08, 2011 at 07:03:01PM -0400, Jason Stover wrote:
>      I wonder if, in the presence of interactions, it would be easier to
>      just encode the means for each factor/level combination, rather than
>      encoding products of explanatory variables.
>      
> I'm not sure what you mean.  Can you give me an example of how it would work?

After thinking about it more, this might not be the way to go, because it 
wouldn't
simplify the necessary assignment of categories to vectors.

But just to explain what I was thinking:

category * result (5 * 3 = 15 means to estimate, one of which is the
intercept):

         a1 --> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
         a2 --> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
         .      .
         .      .
         .      .
         e3 --> 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

In this case, we have the binary vectors giving us the position
of the estimated mean of the factor/level combination, rather
than the position of the estimated coefficient. 

But now I don't think this is any better than the original approach:
This approach trades one problem for another, since we still must
know which of those encodings belong to 'category', which to 'result',
and which to interaction, whereas the original approach takes care of
this problem by giving us identifiable coefficients. The 'means'
approach also (maybe) adds the difficulty of mixing the two approaches
when other variables or covariates are added to the model but not
included in the interaction.