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On nonparametric estimation of the latent distribution for ordinal data

Author

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  • Ghosh, Sujit K.
  • Burns, Christopher B.
  • Prager, Daniel L.
  • Zhang, Li
  • Hui, Glenn

Abstract

Ordinal data collected in surveys often consist of numerical scores that have a natural ordering. Observed values of ordinal variables can be thought of as a manifestation of an underlying continuous latent variable that is related to the observed ordinal variable through a set of threshold values or “cut-points”. The “cut-points” partition the latent variable into intervals corresponding to the observed levels of the ordinal variable. This latent distribution is of interest to researchers for purposes of descriptive statistics and statistical modeling. However, restrictive parametric assumptions about the latent distribution are often not adequate. A nonparametric model based on mixtures of scaled Beta distributions is presented and estimation is carried out using a version of Anderson–Darling statistic-based criteria which is shown to be computationally more efficient than likelihood based criteria. A Monte Carlo simulation shows that the proposed model and estimation method performs well and is robust against any underlying continuous distribution. Several empirical examples based on ordinal data from the household section of the Agricultural Resource Management Survey (ARMS) illustrate the versatility and adaptability of the method in practice.

Suggested Citation

  • Ghosh, Sujit K. & Burns, Christopher B. & Prager, Daniel L. & Zhang, Li & Hui, Glenn, 2018. "On nonparametric estimation of the latent distribution for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 86-98.
    • Handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:86-98
    DOI: 10.1016/j.csda.2017.10.001
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    References listed on IDEAS

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    1. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    2. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    3. Turnbull, Bradley C. & Ghosh, Sujit K., 2014. "Unimodal density estimation using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 13-29.
    4. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
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    Cited by:

    1. Inés M. Varas & Jorge González & Fernando A. Quintana, 2020. "A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 639-666, December.

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