Xuwen Zhu, Ph.D., Department of Mathematics, University of Louisville

"Faculty salary analysis based on mixtures of two-way time series models"

Finite mixtures present a powerful tool for modeling complex heterogeneous data. One of their most important applications is model-based clustering. It assumes that each data group can be reasonably described by one of mixture model components. This establishes a one-to-one relationship between mixture components and clusters. As most of the methodologies developed in this context cater to vector- and matrix-valued data, the need of establishing a mixture model framework suitable for clustering tensor-valued data is of supreme importance. Data collected in 3-dimensional space, or a time series observed in 2-dimensional space give rise to tensor-valued observations. The authors propose a novel way of analyzing self-reported salaries of teaching faculty employed in American institutions grouped under the most recent Carnegie classification. The information is available for thirteen academic years and it is organized by gender and faculty rank. The study aims at identifying cluster of universities with similar salary structure and suggests direction for answering some key questions explaining the variability in salary.

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