[R] Intercept in Model Matrix (Parameters not what I expected)

[Justin Thong]

I have something which has been bugging me and I have even asked this on
cross validated but I did not get a response.  Let's construct a simple
example. Below is the code.

A<-gl(2,4) #factor of 2 levels
B<-gl(4,2) #factor of 4 levels
df<-data.frame(y,A,B)

As you can see, B is nested within A.
The peculiar result I am interested in the output of the model matrix when
I fit for a nested model . *How does R decide what is included inside the
intercept?* Since we are using dummy coding, the coefficients of the model
is interpreted as the difference between a particular level and the
reference level/the intercept for an single factor model. I understand for
model ~A, A1 becomes the intercept and that for model ~A+B, A1 and B1
(both) become the intercept.

*I do not get why when we use a nested model, A1:B2 appears as a column
inside the model matrix. Why isn't the first parameter of the interaction
subspace A1:B1 or A2:B1? *I think I am missing the concept. I think the
intercept is A1. *Hence, Why do we not compare the levels of A1:B1 and
A1(intercept)  or A2:B1 and A1(intercept)?*

#nested model
> mod<-aov(y~A+A:B)
> model.matrix(mod)
  (Intercept) A2 A1:B2 A2:B2 A1:B3 A2:B3 A1:B4 A2:B4
1           1  0     0     0     0     0     0     0
2           1  0     0     0     0     0     0     0
3           1  0     1     0     0     0     0     0
4           1  0     1     0     0     0     0     0
5           1  1     0     0     0     1     0     0
6           1  1     0     0     0     1     0     0
7           1  1     0     0     0     0     0     1
8           1  1     0     0     0     0     0     1


-- 
Yours sincerely,
Justin

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