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dc.contributor.authorWaters, Andrew
Fronczyk, Kassandra
Guindani, Michele
Baraniuk, Richard G.
Vannucci, Marina
dc.date.accessioned 2017-06-14T18:46:24Z
dc.date.available 2017-06-14T18:46:24Z
dc.date.issued 2015
dc.identifier.citation Waters, Andrew, Fronczyk, Kassandra, Guindani, Michele, et al.. "A Bayesian nonparametric approach for the analysis of multiple categorical item responses." Journal of Statistical Planning and Inference, 166, (2015) Elsevier: 52-66. https://doi.org/10.1016/j.jspi.2014.07.004.
dc.identifier.urihttps://hdl.handle.net/1911/94848
dc.description.abstract We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogeneous groups according to their relevant factors. Clustering, in particular, allows us to borrow strength across subjects, therefore helping in the estimation of the model parameters, particularly when the number of observations is small. We employ Markov chain Monte Carlo techniques and obtain tractable posterior inference for our objectives, including sampling of missing data. We demonstrate the effectiveness of our method on simulated data. We also analyze two real-world educational datasets and show that our method outperforms state-of-the-art methods. In the analysis of the real-world data, we uncover hidden relationships between the questions and the underlying educational concepts, while simultaneously partitioning the students into groups of similar educational mastery.
dc.language.iso eng
dc.publisher Elsevier
dc.rights This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
dc.title A Bayesian nonparametric approach for the analysis of multiple categorical item responses
dc.type Journal article
dc.citation.journalTitle Journal of Statistical Planning and Inference
dc.subject.keywordBayesian Nonparamterics
Cluster Analysis
Factor Analysis
Learning Analytics
Multinomial Probit Model
dc.citation.volumeNumber 166
dc.type.dcmi Text
dc.identifier.doihttps://doi.org/10.1016/j.jspi.2014.07.004
dc.identifier.pmcid PMC4612535
dc.identifier.pmid 26500388
dc.type.publication post-print
dc.citation.firstpage 52
dc.citation.lastpage 66


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