# [R] Manova question.

Douglas Bates bates at wisc.edu
Tue Jun 15 19:11:25 CEST 2004

```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
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
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>> http://www.R-project.org/posting-guide.html
>>
>>
> 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)

```