Unfolding-model-based visualization: theory, method and applications

Yunxiao Chen, Zhiliang Ying and Haoran Zhang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal points, with personperson, item-item, and person-item similarities being captured by the Euclidian distances between the points. In this paper, we study the visualization of multidimensional unfolding from a statistical perspective. We cast multidimensional unfolding into an estimation problem, where the respondent and item ideal points are treated as parameters to be estimated. An estimator is then proposed for the simultaneous estimation of these parameters. Asymptotic theory is provided for the recovery of the ideal points, shedding lights on the validity of model-based visualization. An alternating projected gradient descent algorithm is proposed for the parameter estimation. We provide two illustrative examples, one on users’ movie rating and the other on senate roll call voting.

Keywords: multidimensional unfolding; data visualization; distance matrix completion; item response data; embedding (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 52 pages
Date: 2021-01-01
New Economics Papers: this item is included in nep-ecm
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Published in Journal of Machine Learning Research, 1, January, 2021, 22, pp. 1-51. ISSN: 1532-4435

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