Size-correction using regression residuals

[morphmet]

-------- Original Message --------
Subject:        Size-correction using regression residuals
Date:   Wed, 30 Sep 2009 04:28:27 -0700 (PDT)
From:   Rebeca <rrodrig...@iim.csic.es>
To:     <morphmet@morphometrics.org>



Dear morphometricians,



I am studying morphological variation of a fish species around the
Iberian Peninsula in order to identify possible phenotypic stocks, using
13 landmarks to analyze shape. I have samples from 7 different
locations, but as the size composition in my samples differs among
locations, I want to eliminate the variation associated with size before
I do a discriminant analysis.



For that purpose, I have been using the residuals from a multivariate
pooled-within group regression of shape (Procrustes coordinates) on size
(Centroid size) to obtain “size-free” variables that can be used as
input in the discriminant function analysis (DFA).



However, I have noticed that when I use these residuals, the degree of
separation among my samples in the DFA seems to be a bit exaggerated
(i.e. samples that are supposed to be similar appear to be completely
separated from each other).



Because of that, I decided to do an exercise to see the effect of
size-correction on the discrimination of my samples:

First, I separated some specimens from the same location into 2 groups
of “big” and “small” specimens:

Group 1: 74 specimens with a centroid size >20 cm

Group 2: 70 specimens with a centroid size <13 cm



Then, I did a DFA with the 2 groups: first with the shape variables
without size-correction and then using the residuals that I mention above.



As expected, I found differences between the 2 groups when no
size-correction was done, due to the differences in size composition of
the samples.



After size-correction, I expected no differences between the two groups,
since all specimens (big and small) come from the same location;
however, in the DFA the degree of separation between the 2 groups
increased even more than when I used no size-correction!



I am very interested to know if someone has had a similar experience
with size-correction or if anyone can comment on what could be happening
here.



Thanks in advance,

Rebeca





Rebeca P. Rodriguez Mendoza, PhD candidate

Instituto de Investigaciones Marinas CSIC- Fisheries group

C/ Eduardo Cabello, 6

Tel. 986 23 19 30 ext. 240

Fax: 986 29 27 62

36 208 Vigo, ESPAÑA




--
Replies will be sent to the list.
For more information visit http://www.morphometrics.org