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Spline Regression in the Presence of Categorical Predictors


  • Shujie Ma
  • Jeffrey S. Racine
  • Lijian Yang


We consider the problem of estimating a relationship nonparametrically using regression splines when there exist both continuous and categorical predictors. We combine the global properties of regression splines with the local properties of categorical kernel functions to handle the presence of categorical predictors rather than resorting to sample splitting as is typically done to accommodate their presence. The resulting estimator possesses substantially better nite-sample performance than either its frequency-based peer or cross-validated local linear kernel regression or even additive regression splines (when additivity does not hold). Theoretical underpinnings are provided and Monte Carlo simulations are undertaken to assess nite-sample behavior, and two illustrative applications are provided. An implementation in R (R Core Team (2012)) is available; see the R package 'crs' for details (Racine & Nie (2012)).

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  • Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2012. "Spline Regression in the Presence of Categorical Predictors," Department of Economics Working Papers 2012-06, McMaster University.
  • Handle: RePEc:mcm:deptwp:2012-06

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    References listed on IDEAS

    1. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    2. Liu, Rong & Yang, Lijian, 2010. "Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model," Econometric Theory, Cambridge University Press, vol. 26(01), pages 29-59, February.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, December.
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    Cited by:

    1. Paudel, Krishna P. & Lin, C.-Y. Cynthia & Pandit, Mahesh, 2014. "Environmental Kuznets Curve for Water Quality Parameters at Global Level," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162618, Southern Agricultural Economics Association.
    2. Quiroz, Matias & Villani, Mattias & Kohn, Robert, 2015. "Speeding Up Mcmc By Efficient Data Subsampling," Working Paper Series 297, Sveriges Riksbank (Central Bank of Sweden).
    3. Christopher F. Parmeter & Jeffrey S. Racine, 2018. "Nonparametric Estimation and Inference for Panel Data Models," Department of Economics Working Papers 2018-02, McMaster University.
    4. Daniel J. Henderson & Anne-Charlotte Souto, 2018. "An Introduction to Nonparametric Regression for Labor Economists," Journal of Labor Research, Springer, vol. 39(4), pages 355-382, December.
    5. Nicholas M. Kiefer & Jeffrey S. Racine, 2017. "The smooth colonel and the reverend find common ground," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 241-256, March.
    6. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2015. "Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(2), pages 285-315, February.
    7. Pandit, Mahesh & Paudel, Krishna P. & Williams, Deborah, 2014. "Effect of Remittance on Intensity of Agricultural Technology Adoption in Nepal," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162692, Southern Agricultural Economics Association.
    8. Antonio Musolesi & Michel Simioni & Georgios Gioldasis, 2018. "Nonparametric estimation of international R&D spillovers," Working Papers 2018037, University of Ferrara, Department of Economics.
    9. Shujie Ma & Jeffrey S. Racine, 2012. "Additive Regression Splines With Irrelevant Categorical and Continuous Regressors," Department of Economics Working Papers 2012-07, McMaster University.
    10. Shintaro Yamaguchi, 2013. "Changes in Returns to Task-Specific Skills and Gender Wage Gap," Global COE Hi-Stat Discussion Paper Series gd12-275, Institute of Economic Research, Hitotsubashi University.
    11. Jeffrey S. Racine & Qi Li & Li Zheng, 2018. "Optimal Model Averaging of Mixed-Data Kernel-Weighted Spline Regressions," Department of Economics Working Papers 2018-10, McMaster University.
    12. Lien, Donald & Hu, Yue & Liu, Long, 2017. "A note on using ratio variables in regression analysis," Economics Letters, Elsevier, vol. 150(C), pages 114-117.
    13. Shujie Ma & Jeffrey S. Racine & Aman Ullah, 2015. "Nonparametric Regression-Spline Random Effects Models," Department of Economics Working Papers 2015-10, McMaster University.
    14. Geraldine Henningsen & Arne Henningsen & Christian Henning, 2015. "Transaction costs and social networks in productivity measurement," Empirical Economics, Springer, vol. 48(1), pages 493-515, February.
    15. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2018. "Nonparametric estimation of international R&D spillovers," SEEDS Working Papers 0318, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Mar 2018.
    16. repec:spr:jclass:v:35:y:2018:i:1:d:10.1007_s00357-018-9248-z is not listed on IDEAS
    17. Jeffrey S. Racine, 2016. "A Correction to "Generalized Nonparametric Smoothing with Mixed Discrete and Continuous Data" by Li, Simar & Zelenyuk (2014, CSDA)," Department of Economics Working Papers 2016-01, McMaster University.

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