[R] Manova question.
Jens Schumacher
jschum at bgc-jena.mpg.de
Tue Jun 15 17:52:15 CEST 2004
knussear wrote:
> Hi list,
>
> I'm attempting to re-create a Repeated Measures Compositional Analysis as
> described in the work by Aebischer et. al. (Ecology. 1993. 74(5):
> 1313-1325).
>
> In this paper they describe transitions of data into a log ratio
> difference matrix, from which they obtain two matrices using a monova
> routine.
>
> I am able to produce the second of the two matrices, but I'm having
> trouble with the first.
>
> the difference matrix going in is given here.
>
> Animal Scrub Bl wood Con wood Grass
> 1 0.970 -2.380 -5.154 -9.408
> 2 1.217 -0.173 -4.955 -5.521
> 3 1.178 -0.248 -4.089 0.338
> 4 0.520 0.466 -4.801 -1.946
> 5 8.445 9.319 10.753 8.171
> 6 8.654 9.327 10.732 8.152
> 7 8.429 9.350 10.818 8.141
> 8 9.120 9.565 3.813 8.127
> 9 9.227 9.882 3.813 7.779
> 10 9.423 8.086 3.813 8.539
> 11 9.626 9.392 3.813 8.135
> 12 9.234 8.302 3.813 8.537
> 13 8.672 8.908 9.832 8.416
>
>
> And the first of the matrices is given here, and is "matrix of
> mean-corrected sums of squares and cross products calculated from the
> difference matrix."
>
>
> Scrub Bl wood Con wood Grass
> Scrub 179.52 214.59 244.58 273.75
> Bl wood 214.59 268.44 314.35 343.86
> Con wood 244.58 314.35 471.09 400.22
> Grass 273.75 343.86 400.22 477.78
>
>
> From manova on the data set I can get the diagonal of the matrix, but
> not the others.
>
> manova(y ~ NULL)
>
> Terms:
> Residuals
> Scrub 179.5273
> Bl.wood 268.4347
> Con.wood 471.0845
> Grass 477.8014
> Deg. of Freedom 12
>
>
> Could anyone offer a suggestion ?
>
> Thanks
>
>
> Ken
>
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>
Let data.matrix be the above difference matrix. You obtain the "raw
sums of squares and cross-products matrix" by
R2 <- t(data.matrix) %*% data.matrix
or even
R2 <- crossprod(data.matrix, data.matrix)
To obtain the the second matrix you have to repeat the same thing with
matrix of mean-corrected values.
data.centered <- data.matrix - matrix(colMeans(data.matrix),
ncol=ncol(data.matrix),nrow=nrow(data.matrix), byrow=T)
R1 <- t(data.centered) %*% data.centered
HTH
Jens Schumacher
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