-------- Original Message -------- Subject: Re: Angle differences in PC axes Date: Fri, 25 Mar 2011 13:56:26 -0400 From: Dean Adams <[email protected]> To: [email protected] Lissa, The angle found from: arccos(U*V) would be expressed in radians. Thus, taking (180/pi)arccos(U*V) would yield the angle in degrees. If further adjustment to this angle is required (say, to test a particular angular hypothesis), this should be done after the initial calculations. Dean -- Dr. Dean C. Adams Associate Professor Department of Ecology, Evolution, and Organismal Biology Department of Statistics Iowa State University Ames, Iowa 50011 www.public.iastate.edu/~dcadams/ phone: 515-294-3834 On 3/25/2011 7:42 AM, morphmet wrote:
-------- Original Message -------- Subject: Angle differences in PC axes Date: Wed, 23 Mar 2011 14:49:43 -0400 From: Lissa Tallman<[email protected]> To: [email protected] Hello Morphmetricians, I am currently working on a project that compares ontogenetic trajectories in postcranial elements of extant apes using geometric morphometrics. I performed both a common GPA on the entire sample, as well as individual GPAs on each taxon and I've looked at the results in both Procrustes shape space and Procrustes form space. In both cases (particularly once centroid size is included, of course) the bulk of the shape change occurs along the first PC axis. I would like to determine the differences in the angles of those PC axes. In theory, I believe I need to calculate the dot product of the eigenvectors (as the sum of all Ux*Vx), and then take the arccos of that value. If the dot product is greater than 1, I've been assuming that indicates an angle of over 180 degres, and I've been subtracting 2 to take the arcccos of the complimentary angle, and then subtracting that from 180. The problem is that the data from these calculations don't make geometric sense. If I have three taxa, and I am comparing all three of them in a pairwise manner, the sum of the two smaller angles should equal the sum of the largest angle - but that is not what I am getting. I am wondering if I need to apply some kind of transformation to my vectors to make sure that they begin in the same place? I did calculate the magnitude of each vector, and they are all just trivially different from 1. Lissa
