-------- Original Message -------- Subject: RE: regression of Procrustes coordinates on classifiers Date: Fri, 27 Feb 2009 12:35:59 -0800 (PST) From: F. James Rohlf <[email protected]> Reply-To: <[email protected]> Organization: Stony Brook University To: <[email protected]> References: <[email protected]> Not quite correct. Using Hotelling's generalized T^2 statistic would be like using a squared t-test statistic. Using Mahalanobis D^2 (i.e., D squared) is like using the number of standard deviations by which two means differ. That makes it a reasonable squared distance to use in some applications. For example, if you assume a simple equal-rate Brownian-motion random walk as your evolutionary model then time since separation should be proportional to D^2. Using a generalized distance is appropriate here because one assumes there would be more rapid evolution in directions in which there is more variation within populations. On the other hand, if you want an absolute measure of the amount of shape difference between two species then you should use Procrustes distance (not squared). I agree that any "correcting" should be done using linear models on your shape variables in the tangent space (shape coordinates, partial warp scores, etc.). ========================= F. James Rohlf Distinguished Professor, Stony Brook University http://life.bio.sunysb.edu/ee/rohlf
-----Original Message----- From: morphmet [mailto:[email protected]] Sent: Friday, February 27, 2009 1:05 PM To: morphmet Subject: Re: regression of Procrustes coordinates on classifiers -------- Original Message -------- Subject: Re: regression of Procrustes coordinates on classifiers Date: Fri, 27 Feb 2009 07:29:36 -0800 (PST) From: Joseph Kunkel <[email protected]> To: [email protected] CC: Joseph Kunkel <[email protected]> References: <[email protected]> Louis, My first comment is about using Mahalanobis D as a 'distance'. That is really a misnomer. Mahalanobis D is a sum of independent F-tests when you look at how it is calculated. The true distance is perhaps the mean Euclidean distance and Mahalanobis D is the test of whether that Euclidean Distance is actually significantly different from zero. Using Mahalanobis D as a distance is like using a t-test value as a measure of a difference-of-interest. If that is what you want, an abstraction of how many standard deviations you are away from zero that is fine. But remember that F-tests explode (they are ratios of squares so if the denominator is unstable the explosion is greater) when the the null hypothesis is not true! Sorry for sawing an old horse, or am I wrong in a more basic way in this instance? I would export the aligned coordinates, analyze then in a GLM factorial design, remove your 'desert vs forest "factor"' before and after calculating your distance and testing for their significance. To be pedantic for the sake of novice readers of this list: As you suggest, in the General Linear Model, Y = XB, your factors belong on the right in the design matrix X. They are corrected for as factors. Continuous variables belong on the left as columns of the Y matrix and should be eliminated by the generalized test of additional information. (Rao, 1965, Linear Statistical Inference and its Applications) I would avoid the perhaps easier route of analysis and suggest that if MorphoJ wants to include correcting for factors within a comparison group that it be done in a formally correct way. Doing things in convenient ways will take us down the same road traveled by the Windows operating System. Joe On Feb 27, 2009, at 9:01 AM, morphmet wrote: > > > -------- Original Message -------- > Subject: regression of Procrustes coordinates on classifiers > Date: Fri, 27 Feb 2009 05:55:11 -0800 (PST) > From: Louis Boell <[email protected]> > To: <[email protected]> > > > > Dear colleagues, > > I wish to investigate how strongly the fact that a sample of specimens > belongs to a given class, say, samples from desert vs samples from > forest, influences the Mahalanobis distances between my samples. This > amounts to "correcting" for the desert vs forest "factor" > and checking how much smaller the Mahalanobis distances between desert > and forest samples get when calculated from the residuals of the > "correction". > > I have about 10 samples per class (each sample in itself consisting of > enough specimens given the number of landmarks) from each class). > > In this situation, I tried "correction" by using a dummy-coded > regression (desert=1, forest=2) of Procrustes coordinates on my factor > in MorphoJ. The results are appealing. Now I know that for a > noncontinoous independent variable, you´d prefer to use logistic > regression instead of simple regression, because the fit will be more > appropriate in this case. > > My question is: is there a statistical reason not to use this > procedure? > Or caution about the interpretation of the results? > I´d be grateful for any advice > > Best wishes > > Louis > > Louis Boell > MPI für Evolutionsbiologie > August-Thienemannstr.2 > 24306 Plön > [email protected] > [email protected] > > > > ------------------------------------------------------------------ ------ > Sicher, schnell, übersichtlich - der Internet Browser vom Marktführer! > <http://redirect.gimas.net/?n=M0902IE8beta> > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org -·. .· ·. .><((((º>·. .· ·. .><((((º>·. .· ·. .><((((º> .··.· >=- =º}}}}}>< Joseph G. Kunkel, Professor Biology Department University of Massachusetts Amherst Amherst MA 01003 http://www.bio.umass.edu/biology/kunkel/ -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
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