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Subject: Size-correction using regression residuals
Date: Wed, 30 Sep 2009 04:28:27 -0700 (PDT)
From: Rebeca <[email protected]>
To: <[email protected]>
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
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