-------- Original Message --------
Subject: RE: any reason for lineal orthogonal measures?
Date: Wed, 4 Feb 2009 08:09:11 -0800 (PST)
From: Luis Cabo <[email protected]>
Reply-To: <[email protected]>
To: <[email protected]>
References: <[email protected]>
Nestor, I don't know if I am interpreting your question correctly, but
linear measurements are not necessarily orthogonal with respect to each
other. As a matter of fact, they are usually not (in the particular case
of "length" and "width," they are usually correlated). The axes we use
to represent them are, which is not the same thing. Orthogonality is
basically the geometric definition of independence: if the main axis
along your data points (e.g. the regression line) is not orthogonal
(perpendicular) to one of your "plot axes" (and therefore parallel to
the other), your variables, whatever they are, are not orthogonal. So
the same principle (if not exactly the maths, as we start with points in
space, rather than with lines) would work for landmarks. That is
precisely why we study them (the interesting part is the relationship
between our variables, especially from a functional point of view).
Principal components (or relative warps, if I am correct) are orthogonal
by definition, as the new components try to account for the common
variance not already accounted for by the previous PC's, therefore being
independent from each other, but canonical roots, for example, are not
(that's why CVA uses distance measurements such as Mahalanobis
distances, that also account for the "direction" of the distance, rather
than Euclidean ones). To complicate things further, PC's can be
independent (orthogonal) in the pooled group, but not necessarily (at
least from a theoretical point of view) within groups, if more than one
group (sex, species, population...) is represented in your pooled sample.
The reason to use either linear measurements or landmarks is more
related to the amount of information that you are considering (much
higher when using landmark analysis), and the ease to interpret and
explain your results. In general terms, landmarks work better in both
senses, but If you are testing a clearly defined functional model (e.g.
a system of levers, or physical properties such as moments of inertia or
area of cross-cut sections), linear measurements can be easier to fit in
the already defined physical model (but, hey, as you are recording more
information, you can infer linear distances from landmarks, but not
landmarks from linear measurements. So in order to record your data, you
cannot go wrong with landmarks). Another thing to consider is whether
you are going to be comparing your results with previous work based on
linear measurements, in which case you may still want to try both
approaches (linear to test whether your data corroborate or not previous
observations/models, and landmarks to explain those findings).
I hope this has helped, and that I have got your question (and my
answer) right. I look forward to read the answers of more experienced
posters.
Luis Cabo
Dpt. of Applied Forensic Sciences,
Mercyhurst College
[email protected]
-------- Original Message --------
Subject: any reason for lineal orthogonal measures?
Date: Tue, 3 Feb 2009 09:19:53 -0800 (PST)
From: Guillermo CASSINI <[email protected]>
To: [email protected]
References: <[email protected]>
Hi;
I have a doubt. What's the difference between measures taked between
landmarks (i.e. like EDMA) and standard orthogonal measures? There is
any reason for linear measures to be orthogonal (i.e. length and width)?
Should I prefer one of them instead the other? I'm working with limb
bones, and my propose is perform a PCA analysis, and construct some
indexes based on functional approaches.
Thanks in advance
Nestor
--
Replies will be sent to the list.
For more information visit http://www.morphometrics.org
