Common Allometric Component analysis for 2D landmarks

Common Allometric Component (CAC) analysis for landmarks was first suggested by Mitteroecker et al. (2004). The principle is simple and logical: Do a linear regression of shape as a function of size (the allometric component) and then a PCA on the residuals (the residual shape components). The required data are one column of sizes, followed by pairs of columns containing Procrustes-fitted x-y coordinates of the landmarks. The data can be obtained from the original landmarks using the “Transform->Landmarks->Procrustes” function, and selecting “Add size column”. A final feature of CAC analysis is that if groups are specified, then the data are centered on group means prior to analysis, effectively removing inter-group variation.

In Past, you can produce scatter plots of scores on the common allometric component and the residual shape components, and landmark deformations along all components can be visualized using vector displacements and thin-plate spline grids, relative to mean shape.

For computational details, see the Past manual.


Mitteroecker, P., Gunz, P., Bernhard, M., Schaefer, K., Bookstein, F.L. 2004. Comparison of cranial ontogenetic trajectories among great apes and humans. Journal of Human Evolution 46:679-698.

Published Aug. 31, 2020 8:23 PM - Last modified Aug. 31, 2020 8:23 PM