IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v32y2023i4d10.1007_s10260-022-00661-2.html
   My bibliography  Save this article

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

Author

Listed:
  • Viviana Carcaiso

    (University of Padua)

  • Leonardo Grilli

    (University of Florence)

Abstract

The extension of quantile regression to count data raises several issues. We compare the traditional approach, based on transforming the count variable using jittering, with a recently proposed approach in which the coefficients of quantile regression are modelled by parametric functions. We exploit both methods to analyse university students’ data to evaluate the effect of emergency remote teaching due to COVID-19 on the number of credits earned by the students. The coefficients modelling approach performs a smoothing that is especially convenient in the tails of the distribution, preventing abrupt changes in the point estimates and increasing precision. Nonetheless, model selection is challenging because of the wide range of options and the limited availability of diagnostic tools. Thus the jittering approach remains fundamental to guide the choice of the parametric functions.

Suggested Citation

  • Viviana Carcaiso & Leonardo Grilli, 2023. "Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1061-1082, October.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:4:d:10.1007_s10260-022-00661-2
    DOI: 10.1007/s10260-022-00661-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-022-00661-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-022-00661-2?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. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    2. Duncan Lee & Tereza Neocleous, 2010. "Bayesian quantile regression for count data with application to environmental epidemiology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 905-920, November.
    3. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    4. Sara Moreira & Pedro Pita Barros, 2010. "Double health insurance coverage and health care utilisation: evidence from quantile regression," Health Economics, John Wiley & Sons, Ltd., vol. 19(9), pages 1075-1092, September.
    5. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    6. Elisa Rose Birch & Paul W. Miller, 2006. "Student Outcomes At University In Australia: A Quantile Regression Approach," Australian Economic Papers, Wiley Blackwell, vol. 45(1), pages 1-17, March.
    7. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    8. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    9. Paolo Frumento & Matteo Bottai & Iván Fernández-Val, 2021. "Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 783-797, April.
    10. Winkelmann, Rainer, 2006. "Reforming health care: Evidence from quantile regressions for counts," Journal of Health Economics, Elsevier, vol. 25(1), pages 131-145, January.
    11. Paolo Frumento & Matteo Bottai, 2017. "Parametric modeling of quantile regression coefficient functions with censored and truncated data," Biometrics, The International Biometric Society, vol. 73(4), pages 1179-1188, December.
    12. Alison L. Booth & Hiau Joo Kee, 2009. "Intergenerational Transmission of Fertility Patterns," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 183-208, April.
    13. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    14. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
    15. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    16. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    17. Brian J. Reich, 2012. "Spatiotemporal quantile regression for detecting distributional changes in environmental processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(4), pages 535-553, August.
    18. Alfonso Miranda, 2008. "Planned fertility and family background: a quantile regression for counts analysis," Journal of Population Economics, Springer;European Society for Population Economics, vol. 21(1), pages 67-81, January.
    19. Alina Peluso & Veronica Vinciotti & Keming Yu, 2019. "Discrete Weibull generalized additive model: an application to count fertility data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 565-583, April.
    20. Paolo Frumento & Matteo Bottai, 2016. "Parametric modeling of quantile regression coefficient functions," Biometrics, The International Biometric Society, vol. 72(1), pages 74-84, March.
    21. T Gonzalez & M A de la Rubia & K P Hincz & M Comas-Lopez & Laia Subirats & Santi Fort & G M Sacha, 2020. "Influence of COVID-19 confinement on students’ performance in higher education," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-23, October.
    Full references (including those not matched with items on IDEAS)

    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. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    2. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    3. Das, Priyam & Ghosal, Subhashis, 2018. "Bayesian non-parametric simultaneous quantile regression for complete and grid data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 172-186.
    4. Hao, Meiling & Lin, Yuanyuan & Shen, Guohao & Su, Wen, 2023. "Nonparametric inference on smoothed quantile regression process," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    6. Moreira S & Pita Barros P, 2009. "Double coverage and demand for health care: Evidence from quantile regression," Health, Econometrics and Data Group (HEDG) Working Papers 09/21, HEDG, c/o Department of Economics, University of York.
    7. Chawarat Rotejanaprasert & Andrew B. Lawson, 2018. "A Bayesian Quantile Modeling for Spatiotemporal Relative Risk: An Application to Adverse Risk Detection of Respiratory Diseases in South Carolina, USA," IJERPH, MDPI, vol. 15(9), pages 1-15, September.
    8. Henry R. Scharf & Xinyi Lu & Perry J. Williams & Mevin B. Hooten, 2022. "Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data," International Statistical Review, International Statistical Institute, vol. 90(2), pages 328-345, August.
    9. Luke B. Smith & Brian J. Reich & Amy H. Herring & Peter H. Langlois & Montserrat Fuentes, 2015. "Multilevel quantile function modeling with application to birth outcomes," Biometrics, The International Biometric Society, vol. 71(2), pages 508-519, June.
    10. S. Ghasemzadeh & M. Ganjali & T. Baghfalaki, 2022. "Quantile regression via the EM algorithm for joint modeling of mixed discrete and continuous data based on Gaussian copula," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1181-1202, December.
    11. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    12. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    13. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    14. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    15. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    16. A Ford Ramsey, 2020. "Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach," American Journal of Agricultural Economics, John Wiley & Sons, vol. 102(1), pages 220-239, January.
    17. Maricruz Lacalle-Calderon & Manuel Perez-Trujillo & Isabel Neira, 2017. "Fertility and Economic Development: Quantile Regression Evidence on the Inverse J-shaped Pattern," European Journal of Population, Springer;European Association for Population Studies, vol. 33(1), pages 1-31, February.
    18. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    19. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    20. Richard J. Volpe & Timothy A. Park & Fengxia Dong & Helen H. Jensen, 2016. "Somatic cell counts in dairy marketing: quantile regression for count data," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 43(2), pages 331-358.

    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:spr:stmapp:v:32:y:2023:i:4:d:10.1007_s10260-022-00661-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.