A Monte Carlo study of the inferential properties of three methods of shape comparison

Three inferential morphometric methods, Euclidean distance matrix analysis (EDMA), Bookstein's edge-matching method (EMM), and the Procrustes method, were applied to facial landmark data. A Monte Carlo simulation was conducted with three sample sizes, ranging from n = 10 to 50, to assess type I error rates and the power of the tests to detect group differences for two- and three-dimensional representations of forms. Type I error rates for EMM were at or below nominal levels in both two and three dimensions. Procrustes in 2D and EDMA in 2D and 3D produced inflated type I error rates in all conditions, but approached acceptable levels with moderate cell sizes. Procrustes maintained error rates below the nominal levels in 2D. The power of EMM was high compared with the other methods in both 2D and 3D, but, conflicting EMM decisions were provided depending on which pair (2D) or triad (3D) of landmarks were selected as reference points. EDMA and Procrustes were more powerful in 2D data than for 3D data. Interpretation of these results must take into account that the data used in this simulation were selected because they represent real data that might have been collected during a study or experiment. These data had characteristics which violated assumptions central to the methods here with unequal variances about landmarks, correlated errors, and correlated landmark locations; therefore these results may not generalize to all conditions, such as cases with no violations of assumptions. This simulation demonstrates, however, limitations of each procedure that should be considered when making inferences about shape comparisons.