Re: GLM and interactions

[John Darrington]

On Thu, Jul 07, 2011 at 04:09:28PM -0400, Jason Stover wrote:
     
     The binary encoding for category, drug, and the interaction term would
     be something like this:
     
     category:
        1 --> 0
        2 --> 1
     
     drug:
        1 --> 0 0
        2 --> 1 0
        3 --> 0 1
     
     interaction (category * drug):
        1 * 1 --> 0 0
        1 * 2 --> 0 0
        1 * 3 --> 0 0
        2 * 1 --> 0 0
        2 * 2 --> 1 0
        2 * 3 --> 0 1
     
     So, I have just multiplied each of the pairs. Notice most are mapped
     to the origin. This isn't a problem, though, if we just want to test
     for an interaction. If we take X to be our binary variable for
     category, and Y_1, Y_2 for our binary variables for drug, we can write
     our linear model this way:
     
        response = intercept + b_1 * X + b_2 * Y_1 + b_3 * Y_2 + b_4 * X * Y_1 
+ b_5 * X * Y_2 + error
     

How would this encoding look in the more general case where "category" had 
(say) five
distinct values instead of only two?
     

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