Using LASSO to Model Interactions and Nonlinearities in Survey Data

Abstract

The LASSO and its variants have become a core part of the machine learning toolkit. Similar to OLS and logistic regression, the LASSO can be applied to continuous or binary data. The LASSO is a form of penalized regression, shrinking some coefficients exactly to zero. Because of that, it is especially useful for variable selection — for example, in situations where there are many potential covariates, only a few of which are likely relevant. In this article, we introduce the LASSO (and Adaptive LASSO) and show how it can be applied in situations where the researcher thinks the outcome variable is a nonlinear and/or interacted function of the covariates. Our motivating example is survey response. We provide an example showing how to model survey response using the LASSO and a polynomial expansion of the covariates. Our resulting model has better out-of-sample prediction for survey response than does a traditional logistic regression model. Example R code is provided in the supplemental materials.