[R] how to understand the interaction of two fixed effects

[genomenet at gmail.com]

Hi There,

I have two questions about how to understand well about the
interaction efffect.

1) Suppose two factors, A and B.
A has n levels, B has m levels.
Why the degree of freedom of interaction effect of A and B ( here I
mean A:B not A*B) is (n-1)*(m-1) not n*m-1?

2) can Lard:Gender be understood as LardGender?

Value=c(709,679,699,657,594,677,592,538,476,508,505,539)
Lard=rep(c("Fresh","Rancid"),each=6)
Gender=rep(c("Male","Male","NONE","NONE","Female","Female"),2)
LardGender=rep(c("FreshMale","FreshNONE","FreshFemale","RancidMale","RancidNONE","RancidFemale"),each=2)
Food=data.frame(Value,Lard, Gender,LardGender)

Why is the following two return outputs of lm() function different?
> lm(Value~Lard+Gender+Lard:Gender,data=Food)

Call:
lm(formula = Value ~ Lard + Gender + Lard:Gender, data = Food)

Coefficients:
          (Intercept)             LardRancid             GenderMale  
                635.5                 -113.5                   58.5  
           GenderNONE  LardRancid:GenderMale  LardRancid:GenderNONE  
                 42.5                  -15.5                  -72.5  

> lm(Value~Lard+Gender+LardGender,data=Food)

Call:
lm(formula = Value ~ Lard + Gender + LardGender, data = Food)

Coefficients:
           (Intercept)              LardRancid              GenderMale  
                 635.5                  -113.5                    43.0  
            GenderNONE     LardGenderFreshMale     LardGenderFreshNONE  
                 -30.0                    15.5                    72.5  
LardGenderRancidFemale    LardGenderRancidMale    LardGenderRancidNONE  
                    NA                      NA                      NA  

Thank you very much!

Fan