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Mixture Models for Ordinal Data

Author

Listed:
  • Richard Breen

    (Yale University, New Haven, CT, USA, richard.breen@yale.edu)

  • Ruud Luijkx

    (Tilburg University, The Netherlands)

Abstract

Cumulative probability models are widely used for the analysis of ordinal data. In this article the authors propose cumulative probability mixture models that allow the assumptions of the cumulative probability model to hold within subsamples of the data. The subsamples are defined in terms of latent class membership. In the case of the ordered logit mixture model, on which the authors focus here, the assumption of a logistic distribution for an underlying latent dependent variable holds within each latent class, but because the sample then comprises a weighted sum of these distributions, the assumption of an underlying logistic distribution may not hold for the sample as a whole. The authors show that the latent classes can be allowed to vary in terms of both their location and scale and illustrate the approach using three examples.

Suggested Citation

  • Richard Breen & Ruud Luijkx, 2010. "Mixture Models for Ordinal Data," Sociological Methods & Research, , vol. 39(1), pages 3-24, August.
    • Handle: RePEc:sae:somere:v:39:y:2010:i:1:p:3-24
    DOI: 10.1177/0049124110366240
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    Citations

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    Cited by:

    1. Maria Iannario, 2012. "Preliminary estimators for a mixture model of ordinal 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. 6(3), pages 163-184, October.
    2. Maria Iannario & Domenico Piccolo, 2016. "A comprehensive framework of regression models for ordinal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 233-252, August.

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