Social Science Statistics Blog

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22 October 2012

App Stats: Hazlett and Hainmueller on "Kernel Regularized Least Squares: Moving Beyond Linearity and Additivity Without Sacrificing Interpretability"

We hope you can join us this Wednesday, October 24, 2012 for the Applied Statistics Workshop. Chad Hazlett, a Ph.D. student from the Department of Political Science at MIT, will give a presentation entitled "Kernel Regularized Least Squares: Moving Beyond Linearity and Additivity Without Sacrificing Interpretability" (this is joint work with Jens Hainmueller from MIT). A light lunch will be served at 12 pm and the talk will begin at 12.15.

"Kernel Regularized Least Squares: Moving Beyond Linearity and Additivity Without Sacrificing Interpretability"
Chad Hazlett and Jens Hainmueller
Department of Political Science, MIT
CGIS K354 (1737 Cambridge St.)
Wednesday, October 24th, 2012 12.00 pm

Abstract:

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 provide an accessible explanation of the method and argue that it is well suited for social science inquiry because it avoids strong parametric assumptions and still allows for simple interpretation in ways analogous to OLS or other members of the GLM family. We also extend the method in several directions to make it more effective for social inquiry. In particular, we (1) derive new estimators for the pointwise marginal effects and their variances, (2) establish unbiasedness, consistency, and asymptotic normality of the KRLS estimator under fairly general conditions, (3) develop an automated approach to chose smoothing parameters, and (4) provide companion software. We illustrate the use of the methods through several simulations and a real-data example.

Posted by Konstantin Kashin at October 22, 2012 1:17 AM