The ideal solution to this problem may not exist. A better way to think about it is that the formula 2p-4 tells you that the space of all possible shape variation is 10-dimensional in your case. Within that space you can, for example, test for differences in mean shape and test for covariation of shape with various independent variables.
While it sounds quite reasonable to ask on which variables do the shapes vary most, the variables just serve to define the dimensions of shape space - they are not that interesting in themselves taken one at a time. All rotations of shape space describe the same shape variation equally well so there is nothing that special about the set of axes defined by the partial warps. They are just a convenient way to capture the relevant space. It also sounds like a simple and quite reasonable question to ask which landmarks account for most of the shape variation. The problem is that unless one has some fixed reference landmarks that ones knows do not move, the positions of the landmarks are relative to all of the others used in the Procrustes superimposition. One cannot say that a particular landmark or a subset of landmarks moved and the rest did not vary. Saying that the subset stayed fixed and the rest moved will fit the data equally well. I make a few observations about this problem at the end of my recent paper on bias that was published in the American Anthropologist. For the case of just 3 landmarks, you can investigate this problem by performing some simple simulations in the tpsTri program (this feature is somewhat hidden: open the target window and then click on the Options menu and select 'sample scatter'. In the new window generate random samples for various configurations of the three landmarks.). I suspect that the only solution to this problem will be by developing models that constrain the possible types of shape variation that are allowed in a specific application. This is an area where more work is needed. ----------------------- F. James Rohlf State University of New York, Stony Brook, NY 11794-5245 www: http://life.bio.sunysb.edu/ee/rohlf > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > [EMAIL PROTECTED] > Sent: Tuesday, March 02, 2004 11:27 AM > To: [EMAIL PROTECTED] > Subject: a question > > > Dear morphometrician > > I am working on the ants morphometics. > > Seven landmarks in the head region were initially chosen for > the study. Based on the mathematical equation V=2P-4, I have > 10 different variables. Statistical analysis of collected > measurement data shows that the three variables (Y2, X4 and > UNIX) differ the most from sample to sample i.e the values > for Y2, X4 and UNIX vary the most among different samples. My > question at this point is: "How do the results of the > statistical analysis of the variables relate to the chosen > landmarks?". Basically, based on my findings I would like to > draw some conclusions on how the landmarks differ in various > populations, however I am not exactly sure how my data > relates to the initially chosen landmarks. I would very much > appreciate your guidance and feedback regarding this problem. > > > Thanking you in advance > > Leila Sadegh > email: [EMAIL PROTECTED] > == > Replies will be sent to list. > For more information see > http://life.bio.sunysb.edu/morph/morphmet.html> . > == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
