Peng Yu wrote:
Hi,
I want to do ANOVA for nested designs like following. I don't
understand why the matrix (t(X) %*% X) is singular. Can somebody help
me understand it?
Yes:
A=1 is never combined with B=4, B=5, or B=6
A=2 is never combined with B=1, B=2, or B=3
hence you cannot estimate your model since the corresponding columns in
your Design matrix are all zero.
Uwe Ligges
Regards,
Peng
a=2
b=3
n=4
A = as.vector(sapply(1:a,function(x){rep(x,b*n)}))
B = as.vector(sapply(1:(a*b), function(x){rep(x,n)}))
cbind(A,B)
A B
[1,] 1 1
[2,] 1 1
[3,] 1 1
[4,] 1 1
[5,] 1 2
[6,] 1 2
[7,] 1 2
[8,] 1 2
[9,] 1 3
[10,] 1 3
[11,] 1 3
[12,] 1 3
[13,] 2 4
[14,] 2 4
[15,] 2 4
[16,] 2 4
[17,] 2 5
[18,] 2 5
[19,] 2 5
[20,] 2 5
[21,] 2 6
[22,] 2 6
[23,] 2 6
[24,] 2 6
Y = A + B + rnorm(a*b*n)
fr = data.frame(Y=Y,A=as.factor(A),B=as.factor(B))
afit=aov(Y ~ A / B - 1,fr)
X=model.matrix(afit)
solve(t(X) %*% X)
Error in solve.default(t(X) %*% X) :
Lapack routine dgesv: system is exactly singular
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