Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas

Dean, N. and Nugent, R. (2013) Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas. Advances in Data Analysis and Classification, 7(3), pp. 339-357. (doi: 10.1007/s11634-013-0149-z)

Abstract

<br>This paper presents a finite mixture of multivariate betas as a new model-based clustering method tailored to applications where the feature space is constrained to the unit hypercube. The mixture component densities are taken to be conditionally independent, univariate unimodal beta densities (from the subclass of reparameterized beta densities given by Bagnato and Punzo 2013). The EM algorithm used to fit this mixture is discussed in detail, and results from both this beta mixture model and the more standard Gaussian model-based clustering are presented for simulated skill mastery data from a common cognitive diagnosis model and for real data from the Assistment System online mathematics tutor (Feng et al 2009). The multivariate beta mixture appears to outperform the standard Gaussian model-based clustering approach, as would be expected on the constrained space. Fewer components are selected (by BIC-ICL) in the beta mixture than in the Gaussian mixture, and the resulting clusters seem more reasonable and interpretable.</br> <br>This article is in technical report form, the final publication is available at http://www.springerlink.com/openurl.asp?genre=article &id=doi:10.1007/s11634-013-0149-z</br>

• Item Type: Articles
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11634-013-0149-z
• Keywords: Mixture Model Clustering, Multivariate Beta Densities, Skill Set Profiles, Unit Hypercube
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dean, Dr Nema
• Authors: Dean, N., and Nugent, R.
• Subjects: H Social Sciences > HA Statistics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Research Group: Statistical Methodology
• Journal Name: Advances in Data Analysis and Classification
• Journal Abbr.: ADAC
• Publisher: Springer-Verlag Berlin Heidelberg
• ISSN: 1862-5347
• ISSN (Online): 1862-5355
• Copyright Holders: Copyright © 2013 Springer-Verlag Berlin Heidelberg
• First Published: First Published in Advances in Data Analysis and Classification 7(3):339-357
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.