-------- Original Message -------- Subject: RE: Calculating Consensus Shapes Date: Thu, 13 Mar 2008 21:17:58 -0700 (PDT) From: F. James Rohlf <[EMAIL PROTECTED]> Reply-To: [EMAIL PROTECTED] Organization: Stony Brook University To: [email protected] References: <[EMAIL PROTECTED]>
It is important to remember that when we "reference each individual ... to the grand consensus" in the initial Generalized Procrustes Analysis step the purpose is simply to construct a tangent space that gives the best linear approximation to the curved Kendall shape space so that standard linear multivariate statistical methods can be used. That is what the "weight matrix" (scores for the partial warps and uniform component) provides. The "weight matrix" provides a multivariate data matrix that one can analyze using whatever statistical design is appropriate for the data and questions being asked. It might help to think of this step as a preliminary mathematical transformation - not as a statistical analysis (despite the word "analysis" in its name).
In many cases the grand consensus is no longer relevant for the subsequent statistical analyses. In a phylogenetic study one might make statistical comparisons relative to an outgroup. In a developmental study the comparisons might be relative to an early developmental stage. In both cases the comparisons are made within the tangent space. Whether one uses weighted or unweighted means in the statistical analysis depends on the statistical analysis being carried out.
------------------------ F. James Rohlf, Distinguished Professor Ecology & Evolution, Stony Brook University www: http://life.bio.sunysb.edu/ee/rohlf
-----Original Message----- From: morphmet [mailto:[EMAIL PROTECTED] Sent: Thursday, March 13, 2008 10:28 PM To: morphmet Subject: Calculating Consensus Shapes -------- Original Message -------- Subject: Calculating Consensus Shapes Date: Thu, 13 Mar 2008 14:37:58 -0700 (PDT) From: Greiner Thomas <[EMAIL PROTECTED]> To: <[email protected]> When comparing shapes among different groups we usually reference each individual, or the consensus shape of each group, to the grand consensus shape of the data pool. But, what do we do if our groups are of grossly unequal sample sizes? If this were a univariate problem I would be tempted to use weighted means for each group. But, how do we do this with multivariate shape data? Is it important to account for sample size differences when calculating PCA scores? What about when creating the spline deformation grids? Do the common programs that provide consensus shapes already account for potential sample size differences? Is this not as big a problem as I am thinking it might be (I've got groups with sample sizes ranging from 300 to 20)? */Thomas M. Greiner, Ph.D./* Anatomist and Physical Anthropologist Dept. of Health Professions University of Wisconsin - La Crosse 1725 State Street La Crosse, WI 54601 USA Phone: (608) 785-8476 Fax: (608) 785-8460 -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
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