Browsing by Author "Burak, Katherine L."
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Item Open Access Cluster analysis of correlated non-Gaussian continuous data via finite mixtures of Gaussian copula distributions(2019-06-12) Burak, Katherine L.; De Leon, Alexander R.; Wu, Jingjing; Kopciuk, Karen Arlene; Lu, XuewenModel-based cluster analysis in non-Gaussian settings is not straightforward due to a lack of standard models for non-Gaussian data. In this thesis, we adopt the class of Gaussian copula distributions (GCDs) to develop a flexible model-based clustering methodology that can accommodate a variety of correlated, non-Gaussian continuous data, where variables may have different marginal distributions and come from different parametric families. Unlike conventional model-based approaches that rely on the assumption of conditional independence, GCDs model conditional dependence among the disparate variables using the matrix of so-called normal correlations. We outline a hybrid approach to cluster analysis that combines the method of inference functions for margins (IFM) and the parameter-expanded EM (PX-EM) algorithm. We then report simulation results to investigate the performance of our methodology. Finally, we highlight the applications of this research by applying this methodology to a dataset regarding the purchases made by clients of a wholesale distributor.