[R] Behaviour of interactions in glm

[Colin Towers]

Dear All,

I'm struggling a little with the behaviour of R with GLM interactions. In 
particular, I have a dataset with two factors - call them factor A and 
factor B, where I would like to fit a GLM that is factor A + (grouped 
factor A):factor B.

To try to isolate this, I've ignored the original "factor A" part, as that 
I have this as a separate column in my data. So, it looks like I have 
factor A + factor B + factor C:factor B, but I don't want terms for the 
base level of factor B for that factor C:factor B interaction.

An example of the data I'm trying to fit a model to could be as follows:

Record   FactorA   FactorB  Weight  Response
1         1        1        1       0.73
2         1        2        0.5     0
3         1        3        1       1.00
4         2        1        0.33    2.77
5         2        2        0.4     0
6         2        3        5       0

(I've given a sample here, as my data has around 10,000 records and about 
30 columns).

So, I've prepared my data using something similar to:

glmdata <- read.table("C:\\MyData.csv", sep=",", header=TRUE)

glmdata$FactorA <- C(factor(glmdata$FactorA),base=1)
glmdata$FactorB <- C(factor(glmdata$FactorB),base=2)

glmfit <- glm(Response ~ 1 + FactorA:FactorB, family=(Gamma( 
link="log")), weights = Weight, data=glmdata)

After some playing around, I've found I get slightly different results 
with FactorA*FactorB, FactorA+FactorB+FactorA:FactorB, FactorA:FactorB - 
but whatever I do I always get 6 coefficients.

Really what I would like to do is to ask for FactorA*FactorB less the 
entries in the design matrix that I get from FactorA and FactorB. This 
would leave me with the design matrix being:

Record Mean  FactorA2:FactorB1  FactorA2:FactorB3
1      1     0                  0
2      1     0                  0
3      1     0                  0
4      1     1                  0
5      1     0                  0
6      1     0                  1

If anyone has any advice on how I could make this happen, I'd be very 
grateful!

Thanks in advance,
Colin Towers.