Hi Philipp,
I am not worried about the number of variables (although I am not sure
one needs thousands of highly correlated points on a relatively simple
structure and seem to remember that Gunz and you suggest to start with
many and then reduce as appropriate).

Regardless of whether point homology makes sense, I am worried that
many users believe that semilandmarks (maybe after sliding according
to purely mathematical principles) are the same as "traditional
landmarks" with a clear one-to-one correspondence. Even saying that
what's "homologous" is the curve or surface is tricky, because at the
end of the day that curve/surface is discretized using points, shape
distances are based on those points and there are many ways of placing
points with no clear "homology" (figure 7 of Oxnard & O'Higgins,
2009); indeed, in a ontogenetic study of the cranial vault, for
instance, where sutures may become invisible in adults and therefore
cannot be used as a "boundary", semilandmarks close to the sutures may
end up on different bones in different stages/individuals.

Semilandmarks are a fantastic tool, which I am happy to use when
needed, but they have their own limitations, which one should be aware
of.
Cheers

Andrea



On 03/06/2017, mitte...@univie.ac.at <mitte...@univie.ac.at> wrote:
> I think a few topics get mixed up here.
>
> Of course, a sample can be too small to be representative (as in Andrea's
> example), and one should think carefully about the measures to take. It is
> also clear that an increase in sample size reduces standard errors of
> statistical estimates, including that of a covariance matrix and its
> eigenvalues. But, as mentioned by Dean, the standard errors of the
> eigenvalues are of secondary interest in PCA.
>
> If one has a clear expectation about the signal in the data - and if one
> does not aim at new discoveries - a few specific measurements may suffice,
> perhaps even a few distance measurements. But effective exploratory
> analyses have always been a major strength of geometric morphometrics,
> enabled by the powerful visualization methods together with the large
> number of measured variables.
>
> Andrea, I am actually curious what worries you if one "collects between
> 2700 and 10 400 homologous landmarks from each rib" (whatever the term
> "homologous" is supposed to mean here)?
>
> Compared to many other disciplines in contemporary biology and biomedicine,
>
> a few thousand variables are not particularly many. Consider, for instance,
>
> 2D and 3D image analysis, FEA, and all the "omics", with millions and
> billions of variables. In my opinion, the challenge with these "big data"
> is not statistical power in testing a signal, but finding the signal - the
> low-dimensional subspace of interest - in the fist place. But this applies
> to 50 or 100 variables as well, not only to thousands or millions. If no
> prior expectation about this signal existed (which the mere presence of so
> many variables usually implies), no hypothesis test should be performed at
> all. The ignorance of this rule is one of the main reasons why so many GWAS
>
> and voxel-based morphometry studies fail to be replicable.
>
> Best wishes,
>
> Philipp
>
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-- 

Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università
di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 2058472

Adjunct Associate Professor, School of Anatomy, Physiology and Human
Biology, The University of Western Australia, 35 Stirling Highway,
Crawley WA 6009, Australia

E-mail address: alcard...@gmail.com, andrea.card...@unimore.it
WEBPAGE: https://sites.google.com/site/alcardini/home/main

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