I think this is a silly question, but I would like to be sure of my interpretations.
Let's say I have a response variable Y and two explanatory categorical variables A and B. Each of them has 4 categories (but, I am also interested to know what happens with any number of categories).
I want to find which of the 2 variables explains more the variation of Y. A and B are not independent.
I have the following models:
M_0 : Y ~ 1 M_A : Y ~ A M_B : Y ~ B M_AB : Y ~ A+B
And then I calculate AIC for each. Are these interpretations right:
- AIC(A) < AIC(AB) < AIC(B) < M(0) --> A explains more of Y variation than B, so I can get rid out of B?;
- AIC(AB) < AIC(A) < AIC(B) < M(0) --> both A and B explain variations in Y, but A explains more than B?
I am not sure whether I should use AIC, or the p-values (but can I really compare the p-values and conclude which variable affects my response the most?)
To make my point clearer, let's take an example. Let's say I want to explain people's height (Y). My initial explanatory variable is eye color (A : [black-blue-green-brown]). Then I consider hair color (B : [blond-black-red-brown]), which is not independant with eye color. I want to determine whether B explains height better than A, or whether I have to consider both.