----- Forwarded message from andrea cardini <alcard...@gmail.com> -----
Date: Thu, 7 Feb 2013 03:09:25 -0500
From: andrea cardini <alcard...@gmail.com>
Reply-To: andrea cardini <alcard...@gmail.com>
Subject: Re: Bootstrapping with Semi-landmarks
To: morphmet@morphometrics.org
Hi Collin,
If I've got it right, you have two aims: one is
to test the significance of group mean
differences and the other one to see if any of
the unknown groups is closer to one or the other of the two known ones.
First a consideration: unequal N and maybe small
N in some of the groups is never ideal, although
it might often be the reality of the data. Small
N will also very likely lead to large errors in
the estimates of means etc. (Zoomorphology, 126: 121-134.).
For testing group differences, you can do it
pairwise (with a 'correction' for multiple tests)
using permutations (MorphoJ, PAST etc.) or
bootstraps (IMP and probably other programs). [NB
in all the programs I am suggesting, you'll have
to slide (if you slide them) the semilandmarks in
another program.] You can also do a MANOVA using
a resampling approach. The 'old' Morpheus does it
(brief description in Italian Journal of Zoology,
71: 63-72) but especially if you have many 3D
landmarks/semilandmarks it might take really
long. If you need, I can see what the commands
are. PAST might also have something using
permutations and the DOS series of programs
(PERMANOVA etc.) by Marti Anderson will also have
something of this kind. We recently used
PERMANOVA to test measurement error (Franklin et
al. Concordance of traditional osteometric and
volume rendered MSCT interlandmark cranial
measurements. International Journal of Legal
Medicine, in press: DOI:
10.1007/s00414-012-0772-9). That's a different
aim and PERMANOVA requires equal N across groups,
but there should be another program of the same
series which does not need equal N and might be used also without replicas.
Last but not least, R will do everything
(including sliding) but one needs to know the 'language'.
For assessing group similarities, if you were
focusing on individuals, I would have suggested a
classification method like a DA. You're right
that there is a problem when you have many
variables (and maybe small and unequal N) but it
might still be doable after dimensionality
reduction (e.g., using the first appropriate
number of PCs). Dimensionality reduction is
always tricky. There are papers suggesting how to
test the sensitivity of DAs to the inclusion of
more or less variables (including stuff I was
involved in - Journal of Archaeological Science,
38: 3006-3018 and 40: 735-743 - but there's
plenty more in the morphometric and statistical
literature, I am sure). I would also suggest you
to read some of the papers by 'Viennese-Leipzig'
school, where they need to assess where unknown
fossils might belong to. I remember several
articles using ordinations and bootstraps to
estimate confidence regions and at least one or
two where they did DAs on the first few PCs of
shape coordinates from large configurations of
landmarks and semilandmarks. Philipp Gunz or
someone else in the list will be able to suggest the most appropriate refs.
Most of the stuff I know about group similarities
is in taxonomy where simple ordinations and
phenograms were often used to assess group
similarity. These are usually done either in the
original shape space (e.g., a simple PCA of shape
coordinates), and that preserves the original
shape distances, or in a statistical space such
as the DA/CVA space, which maximizes group
differences, makes variation around means
circular but 'distorts' distances and makes quite
a few assumptions (hard to test with small N and
many variables). Klingenberg and Monteiro (2005,
Syst. Biol.) discuss some of the issues with
different spaces and analyses, and Mitteroecker
and Bookstein (Evol Biol (2011) 38:100–114) do it as well.
It's a good idea to do these analyses taking into
consideration sample variation and uncertainties
in estimates of, for instance, mean shapes.
Examples of ordinations of mean shapes with
confidence regions estimated using bootstraps can
be found in some of my papers (e.g., if I
remember well, Journal of Zoological Systematics
and Evolutionary Research, 47: 258–267 and done
with a more sophisticated and certainly more
accurate method in at least one or two old papers
by Leandro Monteiro (again, Leandro can help with
the exact ref. which I can't remember). David
Polly, if I am correct, and I with various
coauthors also use bootstraps to assess the
impact of sampling on phenograms of mean shapes.
The method is described in the Biological Journal
of the Linnean Society, 2008, 93, 813–834 and
it's not the same as the one implemented in PAST:
we bootstrap individuals in samples and
re-estimate means; PAST bootstraps variables -
which is unlikely to be OK for Procrustes shape
data, has a different aim (assessing character
sampling) and is appropriate in other contexts.
I used to do most of these analyses in NTSYSpc
and recently did it for someone else on the list
who was interested in it (but I CANNOT PROMISE TO FIND TIME!).
I am sure there are other options and hope that others will make suggestions.
Good luck.
Cheers
Andrea
PS
With ordinations, you may also want to add a
minimum spanning tree! NTSYSpc does it using the
Procrustes distances; PAST does it but I believe
is using only the distances from the variables
you're plotting (e.g., two PCs). I prefer the
first option as it helps to see distortions due
to dimensionality reduction in scatterplots.
Andrea
At 04:27 07/02/2013, you wrote:
>
>----- Forwarded message from Collin VanBuren
><collin.vanbu...@mail.utoronto.ca> -----
>
> Date: Mon, 4 Feb 2013 19:59:46 -0500
> From: Collin VanBuren <collin.vanbu...@mail.utoronto.ca>
> Reply-To: Collin VanBuren <collin.vanbu...@mail.utoronto.ca>
> Subject: Bootstrapping with Semi-landmarks
> To: "morphmet@morphometrics.org" <morphmet@morphometrics.org>
>
>Hello all,
>
>I am trying to determine if there are
>significant differences between groups (of
>unequal sample sizes) using an outline analysis
>with sliding semi-landmarks. Two of these groups
>are my 'known' groups, and I'm essentially
>trying to determine to which of the 'known'
>groups the other five groups most likely belong
>(i.e., they are unknowns). According to what I'm
>reading, the only (?) way to do this is to
>bootstrap the partial Procrustes distances and
>then use a Goodall's F-test to test for
>significant differences. This method avoids the
>issues semi-landmarks have with degrees of
>freedom, and it is my understanding that I
>cannot run typical statistical analyses on
>semi-landmark datasets because of these issues.
>
>However, I am having issues finding a program
>with which to run this analysis. In IMP, it
>seems a maximum of four groups are allowed, but
>I have seven total (the other issue is that it
>doesn't seem to be letting me open files, but
>I'm still playing around with that). It doesn't
>appear that MorphoJ or any of the R packages
>I've looked at (mostly geomorph and shapes) work
>well with semi-landmarks, at least not for what
>I'm looking to do. Any advice on a way I could
>perform this analysis or an alternative option?
>
>Thank you in advance for your help!
>Collin
>
>----- End forwarded message -----
>
>
----- End forwarded message -----
