Multivariate Data

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The Experts below are selected from a list of 463074 Experts worldwide ranked by ideXlab platform

Douglas G Altman - One of the best experts on this subject based on the ideXlab platform.

Mike Bradburn - One of the best experts on this subject based on the ideXlab platform.

Dean C Adams - One of the best experts on this subject based on the ideXlab platform.

  • a generalized k statistic for estimating phylogenetic signal from shape and other high dimensional Multivariate Data
    Systematic Biology, 2014
    Co-Authors: Dean C Adams
    Abstract:

    Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional Multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the K statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional Multivariate Data. The method (Kmult) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of Kmult remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for Multivariate Data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on Kmult and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in high- dimensional Data. Statistical properties of Kmult were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that Kmult provides a useful means of evaluating phylogenetic signal in high-dimensional Multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders. (Geometric morphometrics; macroevolution; morphological evolution; phylogenetic comparative method.)

  • a method for assessing phylogenetic least squares models for shape and other high dimensional Multivariate Data
    Evolution, 2014
    Co-Authors: Dean C Adams
    Abstract:

    Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly Multivariate Data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high-dimensional Datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as Data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high-dimensional Datasets.

Sharon Love - One of the best experts on this subject based on the ideXlab platform.

Taane G Clark - One of the best experts on this subject based on the ideXlab platform.

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