Manova question.

Jens Schumacher wrote:

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

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)

or, the preferred form,

R2 <- crossprod(data.matrix)