[R-sig-eco] Minimum Number of Observations for pcaCoDa?

[Jari Oksanen]

Rich,

It seems that the robust covariance matrix (? I assume it is that) is not non-negative definite... 

Function robCompositios::pcaCoDa seems to use function princomp of base R (or its stats package) as the engine to get the principal components. If that function is used for raw data, it stops with error message ("'princomp' can only be used with more units than variables") if the number of columns is larger than the number of rows. However, it seems that it may still be able to handle these cases if you use covariance matrix, and the last (ncol > nrow) eigenvalues will be numerically zero -- that is: the covariance matrix is non-negative definite. Normal covariance matrices normally satisfy this (with provision of numerical precision), but it seems that the robust covariance matrix does not.

Actually, the warning is very clear and says: "n < 2 * p, i.e., possibly too small sample size". The condition I put above was only that n < p, but this seems to require that the number of rows is two times higher than the number of columns. Because this was not case, the warning came true and you got an error. So yes, you need more data if you wish to use this tool. 

Cheers, Jari Oksanen
________________________________________
From: r-sig-ecology-bounces at r-project.org <r-sig-ecology-bounces at r-project.org> on behalf of Rich Shepard <rshepard at appl-ecosys.com>
Sent: 21 November 2014 00:08
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] Minimum Number of Observations for pcaCoDa?

   The compositional data sets have few observations: 4 to 7 rows each, but
there are 5 parts (columns) for each row.

   I tried to use the robCompositions function pcaCoDa(). There was an error
and warning generated:

( winters.biplot <- pcaCoDa(winters.coda) )
Error in princomp.default(xilr, covmat = cv, cor = FALSE) :
   covariance matrix is not non-negative definite
In addition: Warning message:
In covMcd(xilr, cor = FALSE) :
   n < 2 * p, i.e., possibly too small sample size

   The matrix for winters.code has the counts:

   filter gather graze predate shred
1      3     27     3      11     1
2      3     28     3      13     2
3      3     43     7      15     1
4      4     54     6      24     3
5      3     26     4      22     5
6      1     39     2      18     2

   Same results with the data file winters.acomp:

          filter    gather      graze   predate      shred
[1,] 0.06666667 0.6000000 0.06666667 0.2444444 0.02222222
[2,] 0.06122449 0.5714286 0.06122449 0.2653061 0.04081633
[3,] 0.04347826 0.6231884 0.10144928 0.2173913 0.01449275
[4,] 0.04395604 0.5934066 0.06593407 0.2637363 0.03296703
[5,] 0.05000000 0.4333333 0.06666667 0.3666667 0.08333333
[6,] 0.01612903 0.6290323 0.03225806 0.2903226 0.03225806
attr(,"class")
[1] "acomp"

   Is there a minimum number of observations for PCA or was I using the
incorrect data format?

Rich

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