Hello, again.
>
> This is not really working. Here what I have for the moment.
>
Right, I've read only half of the description line of function 'poly'. The
other half states that
"These are all orthogonal to the constant polynomial of degree 0."
But not pairwise orthogonal.
You can look for packages implementing Gram-Schmidt orthogonalization
library(sos)
r1 <- findFn('Gram')
r2 <- findFn('Schmidt')
r1 & r2
or use a (time consuming) trick: form a matrix with the first column as x1,
and the others as the
residuals, which are orthogonal, of the regressions of that column with all
the previous ones.
Example:
orthogonal <- function(x){
x <- cbind(1, x)
nc <- ncol(x)
res <- matrix(NA, nrow(x), nc - 1)
res[, 1] <- x[, 2]
if(nc > 2){
for(j in 3:nc)
res[, j - 1] <- lm.fit(x[, 1:(j - 1)], x[, j])$residuals
}
res
}
set.seed(1)
X <- matrix(1:10, ncol=1)
X <- cbind(X, X + rnorm(10), X + rnorm(10))
cor(X)
[,1] [,2] [,3]
[1,] 1.0000000 0.9726364 0.9485793
[2,] 0.9726364 1.0000000 0.8917848
[3,] 0.9485793 0.8917848 1.0000000
Y <- orthogonal(X)
cor(Y)
[,1] [,2] [,3]
[1,] 1.000000e+00 2.804232e-17 -3.758236e-17
[2,] 2.804232e-17 1.000000e+00 -1.492894e-17
[3,] -3.758236e-17 -1.492894e-17 1.000000e+00
This works but I would use a Gram-Schmidt algorithm.
Rui Barradas
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