Dear all, Oliver Betz asked earlier this week why when he carried out a PCA of shapes with 26 landmarks (=78 variables - x,y and z coords)the output in morphologika shows PC loadings for only 75 variables.
I misunderstood his question and thought he was referring to the reduced dimensionality of the shape space consequent on removing size, rotation and translation (ie a loss of 3 dimensions when working in 2D or 7 in 3D) In fact the issue is simply that in tangent projecting, the dimensionality of the data submitted to PCA (the tangent coordinates as opposed to the original Procrustes registered coordinates) is reduced by 3 for 3D data and 2 for 2D data. Thus 78-3=75. Morphologika knows when tangent projection has been carried out and reverses this before plotting shapes in the output window when exploring PCs etc. This is why almost no-one ever notices. I hope this clarifies things Paul O'Higgins -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
