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Kernel-Based Regularized Least Squares in R (KRLS) and Stata (krls)

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  • Ferwerda, Jeremy
  • Hainmueller, Jens
  • Hazlett, Chad J.

Abstract

The Stata package krls as well as the R package KRLS implement kernel-based regularized least squares (KRLS), a machine learning method described in Hainmueller and Hazlett (2014) that allows users to tackle regression and classification problems without strong functional form assumptions or a specification search. The flexible KRLS estimator learns the functional form from the data, thereby protecting inferences against misspecification bias. Yet it nevertheless allows for interpretability and inference in ways similar to ordinary regression models. In particular, KRLS provides closed-form estimates for the predicted values, variances, and the pointwise partial derivatives that characterize the marginal effects of each independent variable at each data point in the covariate space. The method is thus a convenient and powerful alternative to ordinary least squares and other generalized linear models for regression-based analyses.

Suggested Citation

  • Ferwerda, Jeremy & Hainmueller, Jens & Hazlett, Chad J., 2017. "Kernel-Based Regularized Least Squares in R (KRLS) and Stata (krls)," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i03).
    • Handle: RePEc:jss:jstsof:v:079:i03
    DOI: http://hdl.handle.net/10.18637/jss.v079.i03
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    References listed on IDEAS

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    1. Hainmueller, Jens & Hazlett, Chad, 2014. "Kernel Regularized Least Squares: Reducing Misspecification Bias with a Flexible and Interpretable Machine Learning Approach," Political Analysis, Cambridge University Press, vol. 22(2), pages 143-168, April.
    2. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    3. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(3), pages 199-236, July.
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    1. Christopher Hare & Tzu-Ping Liu & Robert N. Lupton, 2018. "What Ordered Optimal Classification reveals about ideological structure, cleavages, and polarization in the American mass public," Public Choice, Springer, vol. 176(1), pages 57-78, July.
    2. Joachim Wagner, 2024. "Estimation of empirical models for margins of exports with unknown non-linear functional forms: A Kernel-Regularized Least Squares (KRLS) approach Evidence from eight European countries," Working Paper Series in Economics 424, University of Lüneburg, Institute of Economics.
    3. Wagner, Joachim, 2024. "Estimation of empirical models for margins of exports with unknown nonlinear functional forms: A Kernel-Regularized Least Squares (KRLS) approach," KCG Working Papers 32, Kiel Centre for Globalization (KCG).
    4. Joachim Wagner, 2024. "Cloud Computing and Extensive Margins of Exports - Evidence for Manufacturing Firms from 27 EU Countries," Working Paper Series in Economics 427, University of Lüneburg, Institute of Economics.
    5. Choi, Yeri & Lee, Sugie, 2020. "The impact of urban physical environments on cooling rates in summer: Focusing on interaction effects with a kernel-based regularized least squares (KRLS) model," Renewable Energy, Elsevier, vol. 149(C), pages 523-534.
    6. Joachim Wagner, 2024. "Robots and Extensive Margins of Exports - Evidence for Manufacturing Firms from 27 EU Countries," Working Paper Series in Economics 426, University of Lüneburg, Institute of Economics.
    7. Kartal, Mustafa Tevfik & Pata, Ugur Korkut & Kılıç Depren, Serpil & Depren, Özer, 2023. "Effects of possible changes in natural gas, nuclear, and coal energy consumption on CO2 emissions: Evidence from France under Russia’s gas supply cuts by dynamic ARDL simulations approach," Applied Energy, Elsevier, vol. 339(C).

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