----- Forwarded message from
GREGORY CAMPBELL
Date: Thu, 14
Jun 2012 04:13:29 -0400
From: GREGORY CAMPBELL
Reply-To: GREGORY CAMPBELL
Subject: Re: random skewers and
allometry
To: "[email protected]"
To: [email protected]
Sent: Monday, 11 June 2012, 8:29
Subject:
random skewers and allometry
----- Forwarded message from Milos
Blagojevic -----
Date: Fri, 8 Jun 2012
06:20:22 -0400
From: Milos Blagojevic
Reply-To: Milos Blagojevic
Subject: random
skewers and allometry
To: morphmet
Considering the ever-lasting question of size vs.
shape variability in the collections of linear measurements I came across these
two contrasting papers.
1. Berner, D., 2011. Size correction in biology:
how reliable are approaches based on (common) principal component analysis?
Oecologia 166, 961–971.
2.
McCoy, M.W., Bolker, B.M., Osenberg, C.W., Miner, B.G., Vonesh, J.R., 2006.
Size correction: comparing morphological traits among populations and
environments. Oecologia 148, 547–554.
Both of them suggest that the
decision on whether to factor-out size variability should be made on the basis
of inter-population comparison (if there are multiple populations). My question
is that common principal components analysis, although providing covariance
matrix similarity with tests, could be substituted with random skewers method of
Cheverud? Now in that substitution we would lost CPC1 which could be used for,
i.e. Burnaby`s back projection (if all populations share the same size/shape
relationship). Could random skewers coefficient be used as a proxy of similarity
in determining whether major axes of variability run parallel or diverge or are
the same? If all of these coefficients be sufficiently high (although robust
test is lacking) would it be safe to assume that whole sample PC1 axis is a
well-fit representation of size variability, that could be used for either
regression or Burnaby projection?
Best regards,
Milos Blagojevic,
Ph.D. student,
Department of Biology and Ecology,
Faculty of Science,
Kragujevac, Serbia.
email: paulidealist.kg.ac.rs; [email protected];
[email protected]
----- End forwarded message
-----
----- End forwarded message
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Dear Milos: I too have been struggling with the
general failure of real-world datasets of organismal dimensions to
have common PC1 vectors in multivariate allometry (i.e.: after
log-transformation), a difficult thing to find halfway through a dissertation (I
am studying ecophenotypic plasticity in mussels). I am also shocked that
there are still no means of using principal components (either major-axis using
co-variance, or reduced major-axis = standardized major-axis, based
on correlation) as proper regressions. By this I mean that PCA fails
as a regression twice: it has no commonly-used test for significant
differences in 'slope' (the vector of maximal co-variance or correlation through
the mean centroid) between categories (different species, different niches,
different
points along an ecological gradient), AND it has no tests for differences
between intercepts (you can think of intercepts as either initial
conditions, or as compensations for differences between samples in mean
centroid; either way they are critical for understanding the general model or
what differs between samples and therefore between species, niches or ecological
gradient). The allometricians amongst you can clearly tell that I follow
Teissier rather than Huxley regarding the importance of intercepts (always trust
the statistician over the biologist).
In the end I had
to use lumpy old o.l.s. regression with categorization, in spite of the
risk that this type of predictive-model fitting will
not characterize well the similtaneous mutual co-variation of all
dimensions. Yes, I know geometric morphometrics is really pretty, but we
really do need the workhorse application of multivariate
allometric regression to be made to work
properly.
And, as a first step in this, have any of
you tried to apply the method of testing for significant
differences between principal components of
KRZANOWSKI,
W.J. 1979. Between-groups comparison of principal components. Journal of the American Statistical
Association 74: 703-707.
Greg Campbell
The Naive Chemist
From:
"[email protected]"
<[email protected]>
Dear Morphometricians,
- random skewers and allometry morphmet_moderator
- Re: random skewers and allometry morphmet_moderator
- Re: random skewers and allometry morphmet_moderator
- Re: random skewers and allometry morphmet_moderator
