Hi There, 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? I know this is a basic statistical question. Please recommend some good websites or books. Thank you very much. Fan
genomenet at gmail.com
2007-Mar-15 00:13 UTC
[R] how to understand the interaction of two fixed effects
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