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A short introduction to splines in least squares regression analysis

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  • Kagerer, Kathrin

Abstract

Splines are an attractive way of flexibly modeling a regression curve since their basis functions can be included like ordinary covariates in regression settings. An overview of least squares regression using splines is presented including many graphical illustrations and comprehensive examples. Starting from two bases that are widely used for constructing splines, three different variants of splines are discussed: simple regression splines, penalized splines and smoothing splines. Further, restrictions such as monotonicity constraints are considered. The presented spline variants are illustrated and compared in a bivariate and a multivariate example with well-known data sets. A brief computational guide for practitioners using the open-source software R is given.

Suggested Citation

  • Kagerer, Kathrin, 2013. "A short introduction to splines in least squares regression analysis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 472, University of Regensburg, Department of Economics.
    • Handle: RePEc:bay:rdwiwi:27968
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    File URL: https://epub.uni-regensburg.de/27968/1/DP472_Kagerer_introduction_splines.pdf
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    References listed on IDEAS

    as
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    4. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    5. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    6. Cao, Yanrong & Lin, Haiqun & Wu, Tracy Z. & Yu, Yan, 2010. "Penalized spline estimation for functional coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 891-905, April.
    7. Manuel Landajo & Javier De Andrés & Pedro Lorca, 2008. "Measuring firm performance by using linear and non‐parametric quantile regressions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 227-250, April.
    8. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    9. Seiya Imoto & Sadanori Konishi, 2003. "Selection of smoothing parameters inB-spline nonparametric regression models using information criteria," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 671-687, December.
    10. Lee, Thomas C. M., 2000. "Regression spline smoothing using the minimum description length principle," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 71-82, May.
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    Cited by:

    1. Kagerer, Kathrin, 2015. "A hat matrix for monotonicity constrained B-spline and P-spline regression," University of Regensburg Working Papers in Business, Economics and Management Information Systems 484, University of Regensburg, Department of Economics.

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    More about this item

    Keywords

    B-spline; truncated power basis; derivative; monotonicity; penalty; smoothing spline; R;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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