Multivariate Regression Models and Geometric Morphometrics: The Search for Causal Factors in the Analysis of Shape

gists (even those familiar with ordinary mul? tivariate analysis) and in part because the possibilities of application have not been ex? tensively explored. Bookstein (1991) defined morphometrics as the statistical analysis of the covariance between shape and causal factors. Thus, it is interesting to be able to examine the in? fluence of factors that might cause shape changes. In geometric terms, the shape of a group of objects can be studied if we remove the effects of location, size, and orientation from the finite representation of the objects (Small, 1996). Even for planar triangles, the simplest entities for which we can study shape, the study of shape differences within or between groups requires the construction of shape spaces defined by a minimum of two variables (Bookstein, 1991). Therefore, any study of shape variation is necessarily multivariate.