lassopack: Model selection and prediction with regularized regression in Stata

Abstract

This article introduces lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. The methods are suitable for the high-dimensional setting where the number of predictors $p$ may be large and possibly greater than the number of observations, $n$. We offer three different approaches for selecting the penalization (`tuning') parameters: information criteria (implemented in lasso2), $K$-fold cross-validation and $h$-step ahead rolling cross-validation for cross-section, panel and time-series data (cvlasso), and theory-driven (`rigorous') penalization for the lasso and square-root lasso for cross-section and panel data (rlasso). We discuss the theoretical framework and practical considerations for each approach. We also present Monte Carlo results to compare the performance of the penalization approaches.