Dear Asta,
I would suggest that if, you want to stick on the discriminant analysis,
you did generalized discriminant analysis, particularly Canonical
Analysis of Principal Coordinates or CAP (Anderson & Robinson 2003,
Anderson & Willis 2003). In this method the discriminant analysis proper
is performed in PCoA space, where you could keep Euclidean distances as
meaure of likelyness between individuals, and for sure that the
unbalance between number of variables or number of samples will not be
as high as I presume you are facing using raw data. Another advantage is
that you can use the free softaware by Marti Anderson (in DOS, but very
friendly).
Please see details in: http://www.stat.auckland.ac.nz/~mja/
Please note that the alternative between discriminant and principal
component analyses does also rely on whether you have an apriori
hypothesis (of differences between groups of samples) or not, respectively.
Salva
Hello,
does anybody have a good suggestion on ordination of populations when
sample sizes per population is small (smaller than the number of
variables). The data is of "traditional" linear measurements.
Possibilities:
1) Normally I would conduct CVA. However NTsys would not do it when
sample sizes are smaller than no variables.
Some other standard packages can overcome this problem. However, as I
was suggested by F.J. Rohlf:
"The mathematical requirement for a CVA to be
possible is for the within-groups degrees of freedom (total n
minus the number of groups) must be equal to or larger than the
number of variables. There are tricks such as using a generalized
inverse rather than an ordinary inverse but one would not want to
trust the results very much. In fact one does not trust the
results statistically unless the degrees of freedom are quite a
bit larger than the number of variables"
2) Do PCA to summarise the information on the first principal
components. Conduct CVA on the first PCA scores. Minus: it is difficult
to find out which of the original variables were important. Moreover,
what if appart for the PC1 (summarising size) other PCs have rather
similar eigenvalues, and there is still a lot of information lost in
discarding them
3) Some other solutions: principal coordinate analysis - does it make sense?
Thanks,
Asta
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Salvador Herrando-Pérez, Biólogo acuático, BSc. MPhil.
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