On 24-Jul-08 15:30:57, Christoph Scherber wrote:
> Dear all,
> I am fitting a multivariate linear model with 7 response variables and
> 1 explanatory variable.
>
> The following matrix P:
>
> P <- cbind(
> c(1,-1,0,0,0,0,0),
> c(2,2,2,2,2,-5,-5),
> c(1,0,0,-1,0,0,0),
> c(-2,-2,0,-2,2,2,2),
> c(-2,1,0,1,0,0,0),
> c(0,-1,0,1,0,0,0))
>
> should consist of orthogonal elements (as can be shown using %*%
> on the individual columns).
> However, when I use
>
> linhyp=linear.hypothesis(model, "explanatory.variable", P=P)
>
> I get an error saying
>
> Error in linear.hypothesis.mlm(mult1, "logdiv", P = P) :
> The error SSP matrix is apparently of deficient rank = 4 < 6
>
> Which I interpret as there are too many non-zero rows in the matrix, P.
>
> Is that correct? And how can I assess if the matrix is orthogonal
> (given that it is non-symmetrical,
> hence det(P) and other matrix operations won?t work)
The matrix has rank 4 (not 6 as I suppose you intended):
svd(P)$d
# [1] 9.123340e+00 3.280954e+00 3.000000e+00 1.732051e+00
# [5] 2.754966e-16 1.315742e-16
The last two eigenvalues are effectively 0.
Also, as I see it the columns of P are not all orthognal to each
other by pairs:
for(i in (1:5)){for(j in ((i+1):6)) print(c(i,j,sum(P[,i]*P[,j])))}
# [1] 1 2 0
# [1] 1 3 1
# [1] 1 4 0
# [1] 1 5 -3
# [1] 1 6 1
# [1] 2 3 0
# [1] 2 4 -28
# [1] 2 5 0
# [1] 2 6 0
# [1] 3 4 0
# [1] 3 5 -3
# [1] 3 6 -1
# [1] 4 5 0
# [1] 4 6 0
# [1] 5 6 0
Am I using the right P?
P
# [,1] [,2] [,3] [,4] [,5] [,6]
# [1,] 1 2 1 -2 -2 0
# [2,] -1 2 0 -2 1 -1
# [3,] 0 2 0 0 0 0
# [4,] 0 2 -1 -2 1 1
# [5,] 0 2 0 2 0 0
# [6,] 0 -5 0 2 0 0
# [7,] 0 -5 0 2 0 0
> Many thanks for your help!
>
> Best wishes
> Christoph.
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Date: 24-Jul-08 Time: 17:16:41
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