05-22-2014 09:31 AM
I am using GLM regression with two class variable A & B. I do want A * B, but not in a explode way. For example, A has 4 elements, and B has 3 elements, I do not want final 4 * 3 = 12 parameters, I want 4 parameters for A and 3 parameters for B, and these 4 parameters times these 3 paramters are my 12 paramters for estimation. In other way, I do not care the correlation between A and B. Thanks.
05-22-2014 09:47 AM
I'm confused. On the one hand, it sounds like you are saying you want the A*B interaction but then it sounds to me like you say you don't want it. If you include the A*B interaction in the model, it will have 12 parameters, some of which cannot be estimated, resulting in (4-1)*(3-1)=6 degrees of freedom (assuming you also include the main effects in the model)
05-22-2014 12:12 PM
This comes under the heading of wild a** guess, or possibly entertaining. Add a dummy variable to the data which always has the value of 1 and use
I have no evidence this will work but should prevent 12 parameters.
05-22-2014 01:02 PM
When you say "I do not care the correlation between A and B", do you mean that you do not care if the effect of B is not the same on every level of A? Or equivalently, if the effect of A is not the same on every level of B? If you do not care or if you want to assume that the effect of A is independent from the effect of B, i.e. that the effect of A and B is simply the sum of the effect of A and the effect of B, then you don't need the interaction effect in your model. [model y = A B;]
If, on the other hand, you don't care about the individual effects of A and B but only care for their combined effect, then you don't need the main effects in your model [model y = A*B;].
But if you can't assume independence (of A and B) or do care about main effects (of A or B), then you need to test the full model [model y = A B A*B;] first.