IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v119y2018icp86-98.html
   My bibliography  Save this article

On nonparametric estimation of the latent distribution for ordinal data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317302098
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.10.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Turnbull, Bradley C. & Ghosh, Sujit K., 2014. "Unimodal density estimation using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 13-29.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    2. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    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. Lu, Lu, 2015. "On the uniform consistency of the Bernstein density estimator," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 52-61.
    5. 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.
    6. Belalia, Mohamed & Bouezmarni, Taoufik & Leblanc, Alexandre, 2017. "Smooth conditional distribution estimators using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 166-182.
    7. Lina Wang & Dawei Lu, 2023. "Application of Bernstein Polynomials on Estimating a Distribution and Density Function in a Triangular Array," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.
    8. Belalia, Mohamed, 2016. "On the asymptotic properties of the Bernstein estimator of the multivariate distribution function," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 249-256.
    9. Manté, Claude, 2015. "Iterated Bernstein operators for distribution function and density estimation: Balancing between the number of iterations and the polynomial degree," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 68-84.
    10. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    11. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    12. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    13. Yuhui Chen & Timothy Hanson & Jiajia Zhang, 2014. "Accelerated hazards model based on parametric families generalized with Bernstein polynomials," Biometrics, The International Biometric Society, vol. 70(1), pages 192-201, March.
    14. Han, Bing & Dalal, Siddhartha R., 2012. "A Bernstein-type estimator for decreasing density with application to p-value adjustments," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 427-437.
    15. Ariane Hanebeck & Bernhard Klar, 2021. "Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1229-1247, December.
    16. Carnicero, José Antonio, 2008. "A semi-parametric model for circular data based on mixtures of beta distributions," DES - Working Papers. Statistics and Econometrics. WS ws081305, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Paolo Brunori & Guido Neidhöfer, 2021. "The Evolution of Inequality of Opportunity in Germany: A Machine Learning Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(4), pages 900-927, December.
    18. Noël Veraverbeke, 2024. "Bernstein estimator for conditional copulas," Statistical Papers, Springer, vol. 65(9), pages 5943-5954, December.
    19. Mark F. J. Steel & Francisco J. Rubio, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 218-222, August.
    20. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:86-98. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.