----- Forwarded message from "K. James
Soda" <[email protected]> -----
Date: Thu, 28 Mar 2013
23:32:42 -0400
From: "K. James Soda" <[email protected]>
Reply-To: "K. James Soda" <[email protected]>
Subject:
Re: CVA vs DA
To: [email protected]
Dear
Eloise,
Actually, cannonical variance analysis is the same as (linear)
discriminate analysis, although I find that the former term is often used to
describe the graphical aspects of the procedure. There are other types of
discriminate function analysis, but the only one with which I am familiar,
quadratic function analysis, might be impractical. Here's a quick explanation
of how they work and differ: Linear discriminate analysis, in a way, tries to
draw lines in sample space that will separate two or more groups. An unknown
data point is placed into sample space, and classified into whichever group has
a mean on the same side of the line(s) as the unknown. The downside is that
linear discriminate analysis was developed under the assumption that every group
has an identical covariance structure; if this is not the case, the method will
not work as well. Quadratic discriminate function analysis does the same thing
as linear discriminate analysis, but instead of drawing lines it will draw
quadratic curves. This means that groups need not have identical covariance
structures, but, as a result, the method involves estimating every covariance
matrix independently, which requires large sample sizes. Unfortunately, what
constitutes a large sample size depends on the number of variables. Since
landmark-based morphometrics tends to have a large number of variables, large
sample sizes are hard to come by (though not impossible).
My advice is
just to try linear discriminate function analysis, and assess how well it
classifies your teeth using a leave-one-out (LOO) cross validation. This
article gives a good overview of how LOO works and why it is
necessary:
Kovarovic, Kris, Leslie C. Aiello, Andrea Cardini,
and Charles A. Lockwood. 2011. “Discriminant function analyses in
archaeology: are classification rates too good to be true? RID
G-9951-2011.” Journal of Archaeological Science 38 (11) (November):
3006-3018. doi:10.1016/j.jas.2011.06.028.
It might take a little bit of
programming though. If you want it, I can provide you with a LOO cross
validation routine I wrote for linear discriminate function analysis in R. If
you are dissatisfied with the results, there are a great deal more
classification methods out there. Slice, Naylor, and I (Soda) have a 2013 SICB
abstract on an alternative method, though I don't think the abstract has
appeared in SICB's journal yet. If you can find a copy of the conference
proceedings, it is in there, though.
As far as your question about
regression, it may not matter that the teeth are different sizes unless you are
interested in size itself as a variable. For example, if you wanted to regress
shape onto calcium content or something to that degree I do not see why you
would not be able to.
Long answer to a short question, huh? Hope it was
helpful.
James
----- Forwarded message from Eloise Cave <[email protected]> -----
Date: Thu, 28 Mar 2013 11:11:43 -0400
From: Eloise Cave <[email protected]>
Reply-To: [email protected]
Subject: CVA vs DA
To: [email protected]Greetings,
I am trying to determine the difference in shape in stingray teeth between mating season and non mating season. I was wondering which test would be best to perform, canonical variate analysis or discriminant analysis? Also is regression a good idea since I do not have a scale with my samples and my samples are different sizes?Thank You,Eloise CaveFlorida Atlantic University
----- End forwarded message -----
----- End forwarded message
-----
