A critical review of the mean measure of divergence and Mahalanobis distances using artificial data and new approaches to the estimation of biodistances employing nonmetric traits.

This article reviews the two most common distance measures employed for the calculation of biodistances based on nonmetric traits, the mean measure of divergence (MMD) and the tetrachoric Mahalanobis D(2) distance (TMD). In addition, two new approaches for the estimation of biodistances from nonmetric traits are proposed and assessed. The first (OMD) is based on the direct application of the Mahalanobis distance to ordinally recorded data before their transformation to binary dichotomies. The second (RMD) approximates the covariances of the Mahalanobis distance by the Pearson correlation coefficients calculated in the binary dataset. The application of all four methods to artificial datasets demonstrates that they overall provide a satisfactory estimation of the biodistance among samples especially when the number of statistically non significant distances is very limited. However, the best performance is observed by the OMD, whereas special attention should be paid to the TMD since its values might come out of an ill-conditioned system. The influence of the number of traits, the effect of missing values, as well as the validity of the test statistics used to assess biodistance significance are also examined and discussed.