A Comparison of Different Approaches to Unravel the Latent Structure within Metabolic Syndrome

Background: Exploratory factor analysis is a commonly used statistical technique in metabolic syndrome research to uncover latent structure amongst metabolic variables. The application of factor analysis requires methodological decisions that reflect the hypothesis of the metabolic syndrome construct. These decisions often raise the complexity of the interpretation from the output. We propose two alternative techniques developed from cluster analysis which can achieve a clinically relevant structure, whilst maintaining intuitive advantages of clustering methodology. Methods: Two advanced techniques of clustering in the VARCLUS and matroid methods are discussed and implemented on a metabolic syndrome data set to analyze the structure of ten metabolic risk factors. The subjects were selected from the normative aging study based in Boston, Massachusetts. The sample included a total of 847 men aged between 21 and 81 years who provided complete data on selected risk factors during the period 1987 to 1991. Results: Four core components were identified by the clustering methods. These are labelled obesity, lipids, insulin resistance and blood pressure. The exploratory factor analysis with oblique rotation suggested an overlap of the loadings identified on the insulin resistance and obesity factors. The VARCLUS and matroid analyses separated these components and were able to demonstrate associations between individual risk factors. Conclusions: An oblique rotation can be selected to reflect the clinical concept of a single underlying syndrome, howeve

Structures of Multivariate Dependence

The investigation of dependence structures plays a major role in contemporary statistics. During the last decades, numerous dependence measures for both univariate and multivariate random variables have been established. In this thesis, we study the distance correlation coefficient, a novel measure of dependence for random vectors of arbitrary dimension, which has been introduced by Szekely, Rizzo and Bakirov and Szekely and Rizzo. In particular, we define an affinely invariant version of distance correlation and calculate this coefficient for numerous distributions: for the bivariate and the multivariate normal distribution, for the multivariate Laplace and for certain bivariate gamma and Poisson distributions. Moreover, we present a useful series representation of distance covariance for the class of Lancaster distributions and derive a generalization of an integral, which plays a fundamental role in the theory of distance correlation. We further investigate a variable clustering problem, which arises in low rank Gaussian graphical models. In the case of fixed sample size, we discover that this problem is mathematically equivalent to the subspace clustering problem of data for independent subspaces. In the asymptotic setting, we derive an estimator, which consistently recovers the cluster structure in the case of noisy data