References (38)



Kernel Regularized Least Squares: Reducing Misspecification Bias with a Flexible and Interpretable Machine Learning Approach

Jens Hainmueller

Stanford University - Department of Political Science; Stanford Graduate School of Business; Stanford Immigration Policy Lab

Chad Hazlett


Sept 2013

Political Analysis (2013 Forthcoming)

We propose the use of Kernel Regularized Least Squares (KRLS) for social science modeling and inference problems. KRLS borrows from machine learning methods designed to solve regression and classification problems without relying on linearity or additivity assumptions. The method constructs a flexible hypothesis space that uses kernels as radial basis functions and finds the best-fitting surface in this space by minimizing a complexity-penalized least squares problem. We argue that the method is well-suited for social science inquiry because it avoids strong parametric assumptions, yet allows interpretation in ways analogous to generalized linear models while also permitting more complex interpretation to examine non-linearities, interactions, and heterogeneous effects. We also extend the method in several directions to make it more effective for social inquiry, by (1) deriving estimators for the pointwise marginal effects and their variances, (2) establishing unbiasedness, consistency, and asymptotic normality of the KRLS estimator under fairly general conditions, (3) proposing a simple automated rule for choosing the kernel bandwidth, and (4) providing companion software. We illustrate the use of the method through simulations and empirical examples.

Number of Pages in PDF File: 42

Keywords: regression, classification, machine learning, prediction

JEL Classification: C14, C21

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Date posted: April 25, 2012 ; Last revised: September 26, 2013

Suggested Citation

Hainmueller, Jens and Hazlett, Chad, Kernel Regularized Least Squares: Reducing Misspecification Bias with a Flexible and Interpretable Machine Learning Approach (Sept 2013). Political Analysis (2013 Forthcoming). Available at SSRN: https://ssrn.com/abstract=2046206 or http://dx.doi.org/10.2139/ssrn.2046206

Contact Information

Jens Hainmueller (Contact Author)
Stanford University - Department of Political Science ( email )
Stanford, CA 94305
United States
HOME PAGE: http://www.stanford.edu/~jhain/
Stanford Graduate School of Business ( email )
655 Knight Way
Stanford, CA 94305-5015
United States

Stanford Immigration Policy Lab
30 Alta Road
Stanford, CA 94305
United States
Chad Hazlett
UCLA ( email )
405 Hilgard Ave.
Los Angeles, CA 90095-1472
United States
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References:  38