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Biclustering Models for Two-Mode Ordinal Data

Author

Listed:
  • Eleni Matechou

    (University of Kent)

  • Ivy Liu

    (Victoria University of Wellington)

  • Daniel Fernández

    (Victoria University of Wellington)

  • Miguel Farias

    (Coventry University)

  • Bergljot Gjelsvik

    (University of Oxford
    University of Oslo)

Abstract

The work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two-mode ordinal categorical response data, such as those resulting from Likert scale responses. We use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data. Model-fitting is performed using the EM algorithm, and a fuzzy allocation of rows and columns to corresponding clusters is obtained. The clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets.

Suggested Citation

  • Eleni Matechou & Ivy Liu & Daniel Fernández & Miguel Farias & Bergljot Gjelsvik, 2016. "Biclustering Models for Two-Mode Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 611-624, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-016-9503-3
    DOI: 10.1007/s11336-016-9503-3
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    References listed on IDEAS

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    1. Rocci, Roberto & Vichi, Maurizio, 2008. "Two-mode multi-partitioning," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1984-2003, January.
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    4. van Dijk, A. & van Rosmalen, J.M. & Paap, R., 2009. "A Bayesian approach to two-mode clustering," Econometric Institute Research Papers EI 2009-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
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    Cited by:

    1. Roy Costilla & Ivy Liu & Richard Arnold & Daniel Fernández, 2019. "Bayesian model-based clustering for longitudinal ordinal data," Computational Statistics, Springer, vol. 34(3), pages 1015-1038, September.
    2. Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    3. Daniel Fernández & Richard Arnold & Shirley Pledger & Ivy Liu & Roy Costilla, 2019. "Finite mixture biclustering of discrete type multivariate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 117-143, March.

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