Distance-based tests for homogeneity of multivariate dispersions

@article{817, abstract = {The traditional likelihood-based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero-inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non-Euclidean dissimilarity would be more appropriate. Distance-based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene’s test, with P-values obtained either using the traditional F-distribution or using permutation of either least-squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Ni˜no. Monte Carlo simulations from the real data sets show that the distance-based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.}, author = {Anderson, M. J. }, citeulike-article-id = {2625941}, journal = {Biometrics}, keywords = {2\_stat, analysis, biodiversity, coordinates, dissimilarity, heterogeneity, levenes, levenes-test, methods, multivariate, pco, permutation, principal, robust, test, tests}, number = {1}, pages = {245--253}, posted-at = {2008-04-03 13:29:10}, priority = {0}, title = {Distance-based tests for homogeneity of multivariate dispersions}, volume = {62}, year = {2006} }

TY - JOUR ID - 817 L3 - citeulike-article-id:2625941 TI - Distance-based tests for homogeneity of multivariate dispersions JF - Biometrics VL - 62 IS - 1 SP - 245 EP - 253 N2 - The traditional likelihood-based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero-inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non-Euclidean dissimilarity would be more appropriate. Distance-based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene’s test, with P-values obtained either using the traditional F-distribution or using permutation of either least-squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Ni˜no. Monte Carlo simulations from the real data sets show that the distance-based tests are robust and powerful for relevant alternative hypotheses of real differences in spread. KW - 2_stat KW - analysis KW - biodiversity KW - coordinates KW - dissimilarity KW - heterogeneity KW - levenes KW - levenes-test KW - methods KW - multivariate KW - pco KW - permutation KW - principal KW - robust KW - test KW - tests AU - Anderson, MJ PY - 2006/// ER -