IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp1-14.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this article

Copula based generalized additive models for location, scale and shape with non-random sample selection

Author

Listed:
  • Wojtyś, Małgorzata
  • Marra, Giampiero
  • Radice, Rosalba

Abstract

Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. An extension of the generalized additive models for location, scale and shape which accounts for non-random sample selection by introducing a selection equation is discussed. The proposed approach allows for potentially any parametric distribution for the outcome variable, any parametric link function for the selection equation, several dependence structures between the (outcome and selection) equations through the use of copulae, and various types of covariate effects. Using a special case of the proposed model, it is shown how the score equations are corrected for the bias deriving from non-random sample selection. Parameter estimation is carried out within a penalized likelihood based framework. The empirical effectiveness of the approach is demonstrated through a simulation study and a case study. The models can be easily employed via the gjrm() function in the R package GJRM.

Suggested Citation

  • Wojtyś, Małgorzata & Marra, Giampiero & Radice, Rosalba, 2018. "Copula based generalized additive models for location, scale and shape with non-random sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 1-14.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:1-14
    DOI: 10.1016/j.csda.2018.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301026
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.05.001?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. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Chen, Songnian & Zhou, Yahong, 2010. "Semiparametric and nonparametric estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 157(1), pages 143-150, July.
    3. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    4. Ding, Peng, 2014. "Bayesian robust inference of sample selection using selection-t models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 451-464.
    5. Lee, Lung-Fei, 1994. "Semiparametric instrumental variable estimation of simultaneous equation sample selection models," Journal of Econometrics, Elsevier, vol. 63(2), pages 341-388, August.
    6. repec:cup:cbooks:9780521780506 is not listed on IDEAS
    7. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    8. Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
    9. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.
    10. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    11. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, June.
    12. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    13. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    14. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    15. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    16. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    17. Wojtyś, Magorzata & Marra, Giampiero & Radice, Rosalba, 2016. "Copula Regression Spline Sample Selection Models: The R Package SemiParSampleSel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i06).
    18. Marra, Giampiero & Radice, Rosalba, 2013. "Estimation of a regression spline sample selection model," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 158-173.
    19. repec:cup:cbooks:9780521785167 is not listed on IDEAS
    20. Zhang, Rong & Inder, Brett A. & Zhang, Xibin, 2015. "Bayesian estimation of a discrete response model with double rules of sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 81-96.
    21. Margarita Genius & Elisabetta Strazzera, 2008. "Applying the copula approach to sample selection modelling," Applied Economics, Taylor & Francis Journals, vol. 40(11), pages 1443-1455.
    22. Lewis, H Gregg, 1974. "Comments on Selectivity Biases in Wage Comparisons," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1145-1155, Nov.-Dec..
    23. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    24. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    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. Maciej Berȩsewicz & Dagmara Nikulin, 2021. "Estimation of the size of informal employment based on administrative records with non‐ignorable selection mechanism," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 667-690, June.
    2. Wiemann, Paul F.V. & Klein, Nadja & Kneib, Thomas, 2022. "Correcting for sample selection bias in Bayesian distributional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Maciej Berk{e}sewicz & Dagmara Nikulin, 2019. "Estimation of the size of informal employment based on administrative records with non-ignorable selection mechanism," Papers 1906.10957, arXiv.org.
    4. Ibrahim Niankara, 2022. "Government and private sectors' electronic transfer practices and financial inclusion in the economic community of the West African States," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4018-4047, October.

    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. Karol Wyszynski & Giampiero Marra, 2018. "Sample selection models for count data in R," Computational Statistics, Springer, vol. 33(3), pages 1385-1412, September.
    2. Wiemann, Paul F.V. & Klein, Nadja & Kneib, Thomas, 2022. "Correcting for sample selection bias in Bayesian distributional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    4. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    5. Marra Giampiero & Radice Rosalba, 2017. "A joint regression modeling framework for analyzing bivariate binary data in R," Dependence Modeling, De Gruyter, vol. 5(1), pages 268-294, December.
    6. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    7. Emmanuel O. Ogundimu & Jane L. Hutton, 2016. "A Sample Selection Model with Skew-normal Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 172-190, March.
    8. Seonho Shin, 2022. "To work or not? Wages or subsidies?: Copula-based evidence of subsidized refugees’ negative selection into employment," Empirical Economics, Springer, vol. 63(4), pages 2209-2252, October.
    9. Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    10. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    11. Victor Chernozhukov & Ivan Fernandez-Val & Siyi Luo, 2018. "Distribution regression with sample selection, with an application to wage decompositions in the UK," CeMMAP working papers CWP68/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Zhewen Pan, 2023. "On semiparametric estimation of the intercept of the sample selection model: a kernel approach," Papers 2302.05089, arXiv.org.
    13. Pierfrancesco Alaimo Di Loro & Daria Scacciatelli & Giovanna Tagliaferri, 2023. "2-step Gradient Boosting approach to selectivity bias correction in tax audit: an application to the VAT gap in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 237-270, March.
    14. Schwiebert, Jörg, 2012. "Analyzing the Composition of the Female Workforce - A Semiparametric Copula Approach," Hannover Economic Papers (HEP) dp-503, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    15. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    16. Marra, Giampiero & Radice, Rosalba, 2013. "Estimation of a regression spline sample selection model," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 158-173.
    17. Adelchi Azzalini & Hyoung-Moon Kim & Hea-Jung Kim, 2019. "Sample selection models for discrete and other non-Gaussian response variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 27-56, March.
    18. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    19. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity in sample selection models," Economics Working Paper Series 1145, University of St. Gallen, School of Economics and Political Science.
    20. Wojtyś, Magorzata & Marra, Giampiero & Radice, Rosalba, 2016. "Copula Regression Spline Sample Selection Models: The R Package SemiParSampleSel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i06).

    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:127:y:2018:i:c:p:1-14. 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.