----- Forwarded
message from Peter
Claes
Date: Tue, 19 Jun 2012
13:42:33 -0400
From: Peter Claes
Reply-To: Peter Claes
Subject: Re: random
skewers and allometry
To:
morphmet@morphometrics.org
Dear
Greg,
I have recently used the work of Krzanowski (1979)
that you mention and his associated paper: Krzanowski (1993): permutational
tests for correlation matrices: Stat Comput 3, 37-44 into the framework of
geometric morphometrics to test for sexual dimorphism in sample covariance
orientation:
Claes P., Walters M., Shriver, M., Puts, D., Gibson, G.,
Clement, J., Baynam, G., Verbeke, G., Vandermeulen, D. and Suetens, P.
Sexual Dimorphism in multiple aspects of 3D Facial symmetry and asymmetry
defined by spatially dense geometric morphometrics, Journal of Anatomy,
2012, in press, doi: 10.1111/j.1469-7580.2012.01528.x (avalaible in early view
section of the journal)
All the Best
Peter
On Mon, Jun 18, 2012 at 7:53 PM, <morphmet_modera...@morphometrics.org>
wrote:
----- 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: "morphmet@morphometrics.org"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 ofKRZANOWSKI, W.J. 1979. Between-groups comparison of principal components. Journal of the American Statistical Association 74: 703-707.Greg CampbellThe Naive ChemistFrom: "morphmet_modera...@morphometrics.org" <morphmet_modera...@morphometrics.org>
To: morphmet@morphometrics.org
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: morphmetDear Morphometricians,
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; paulideali...@gmail.com; spearsata...@hotmail.com
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