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

Author

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  • Chen, Yunxiao
  • Ying, Zhiliang
  • Zhang, Haoran

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.

Suggested Citation

  • Chen, Yunxiao & Ying, Zhiliang & Zhang, Haoran, 2021. "Unfolding-model-based visualization: theory, method and applications," LSE Research Online Documents on Economics 108876, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:108876
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    File URL: http://eprints.lse.ac.uk/108876/
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    References listed on IDEAS

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    1. Frank Busing & Patrick Groenen & Willem Heiser, 2005. "Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 71-98, March.
    2. de Leeuw, Jan & Mair, Patrick, 2009. "Multidimensional Scaling Using Majorization: SMACOF in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i03).
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    Cited by:

    1. Ling Chen & Yuqi Gu, 2024. "A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 626-657, June.

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    More about this item

    Keywords

    multidimensional unfolding; data visualization; distance matrix completion; item response data; embedding;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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