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A critical review of the mean measure of divergence and M ahalanobis distances using artificial data and new approaches to the estimation of biodistances employing nonmetric traits
Author(s) -
Nikita Efthymia
Publication year - 2015
Publication title -
american journal of physical anthropology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.146
H-Index - 119
eISSN - 1096-8644
pISSN - 0002-9483
DOI - 10.1002/ajpa.22708
Subject(s) - mahalanobis distance , divergence (linguistics) , statistics , measure (data warehouse) , mathematics , pearson product moment correlation coefficient , correlation , binary number , transformation (genetics) , estimation , binary data , pattern recognition (psychology) , artificial intelligence , computer science , data mining , biology , philosophy , linguistics , geometry , arithmetic , biochemistry , gene , management , economics
ABSTRACT 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. Am J Phys Anthropol 157:284–294, 2015. © 2015 Wiley Periodicals, Inc.