Relationships between shape variables

En la lista de Morphmet ha surgido esta muy educada e interesante cuestión.
Espero sea de utilidad a los lectores del blog.

Relationships between shape variables
Date: Tue, 2 Dec 2008 16:59:21 -0800 (PST)
From: Brendan McCane <[EMAIL PROTECTED]>
To: morphmet@morphometrics.org

G'day,

I have a rather technical question (i.e. I'm interested in the
underlying technique rather than software that can do it). Here is the
problem:

Given a sample of images (say lateral images of the human facial
skeleton), we locate quite a number of landmarks (actually
semi-landmarks or slid-landmarks) with landmarks coming from many
different structures. I'd like to test for relationships between the
structures - i.e. do changes in this structure (e.g mandible) , produce
corresponding changes in that structure (e.g. upper dentition). Of
course I can do a Procrustes analysis, followed by a PCA and visually
see how the structures co-vary along the principal axes, but I am
interested in something a little less qualitative, perhaps more along
the lines of a hypothesis test. I was thinking perhaps of canonical
correlation analysis between different sets of structures, but I haven't
seen much work using this technique in shape analysis. Does anyone have
any advice or pointers to other work?

--
Cheers,

Brendan.
----------------------------------------------------------------------------
Brendan McCane, Head of Dept, Email: [EMAIL PROTECTED]
Department of Computer Science Phone: +64 3 479 8588/8578.
University of Otago Fax: +64 3 479 8529
Box 56, Dunedin, New Zealand.

-----------------------------------------------------------------------------------------------
From: Dennis E. Slice <[EMAIL PROTECTED]>
To: morphmet@morphometrics.org
References: <[EMAIL PROTECTED]>

The answer you seek can be found in Partial Least-Squares Analysis. See
below to get you started.

Bookstein, FL, P Gunz, P Mitteroecker, et al. 2003. Cranial
integration in Homo: singular warps analysis of the midsagittal plane in
ontogeny and evolution. JOURNAL OF HUMAN EVOLUTION 44, no. 2 (February):
167-187.

Mitteroecker, P, and F Bookstein. 2007. The conceptual and statistical
relationship between modularity and morphological integration.
SYSTEMATIC BIOLOGY 56, no. 5 (October): 818-836.

---. 2008. The evolutionary role of modularity and integration in the
hominoid cranium. EVOLUTION 62, no. 4 (April): 943-958.

Rohlf, FJ, and M Corti. 2000. Use of two-block partial least-squares
to study covariation in shape. SYSTEMATIC BIOLOGY 49, no. 4 (December):
740-753.

Best, dslice
---------------------------------------------------------------------------------
From: Chris Klingenberg <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
Organization: University of Manchester
To: morphmet@morphometrics.org
References: <[EMAIL PROTECTED]>

Hi Brendan

Probably the most widespread technique for this is PLS. A good review of
the technique is the following paper:
Rohlf, F. J., and M. Corti. 2000. The use of two-block partial
least-squares to study covariation in shape. Systematic Biology 49:740–753.



PLS has been used for landmarks in separate configurations, for which
separate Procrustes fits are used. A couple of examples of this:

Tabachnick, R. E., and F. L. Bookstein. 1990. The structure of
individual variation in Miocene Globorotalia. Evolution 44:416–434.

Bastir, M., and A. Rosas. 2005. Hierarchical nature of morphological
integration and modularity in the human posterior face. American Journal
of Physical Anthropology 128:26–34.



A different option is the approach of using a single Procrustes fit for
all landmarks, and then a PLS analysis among sets of landmarks within
the configuration. Examples include:

Klingenberg, C. P., and S. D. Zaklan. 2000. Morphological integration
between developmental compartments in the Drosophila wing. Evolution
54:1273–1285.

Bookstein, F. L., P. Gunz, P. Mitteroecker, H. Prossinger, K. Schaefer,
and H. Seidler. 2003. Cranial integration in Homo: singular warps
analysis of the midsagittal plane in ontogeny and evolution. Journal of
Human Evolution 44:167–187.


Statistical testing is usually done via permutation methods.

I hope this is useful.

Best wishes,
Chris