LASSOPACK: Stata module for lasso, square-root lasso, elastic net, ridge, adaptive lasso estimation and cross-validation

LASSOPACK is a suite of programs for penalized regression methods suitable for the high-dimensional setting where the number of predictors p may be large and possibly greater than the number of observations. LASSOPACK supports both lasso and logistic lasso regression. The package consists of six main programs: lasso2 implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. cvlasso supports K-fold cross-validation and rolling cross-validation for cross-section, panel and time-series data. rlasso implements theory-driven penalization for the lasso and square-root lasso for cross-section and panel data. lassologit, cvlassologit and rlassologit are the corresponding programs for logistic lasso regression. The lasso (Least Absolute Shrinkage and Selection Operator, Tibshirani 1996), the square-root-lasso (Belloni et al. 2011) and the adaptive lasso (Zou 2006) are regularization methods that use L1 norm penalization to achieve sparse solutions: of the full set of p predictors, typically most will have coefficients set to zero. Ridge regression (Hoerl & Kennard 1970) relies on L2 norm penalization; the elastic net (Zou & Hastie 2005) uses a mix of L1 and L2 penalization. lasso2 implements all these estimators. rlasso uses the theory-driven penalization methodology of Belloni et al. (2012, 2013, 2014, 2016) for the lasso and square-root lasso. cvlasso implements K-fold cross-validation and h-step ahead rolling cross-validation (for time-series and panel data) to choose the penalization parameters for all the implemented estimators. lassologit, rlassologit and cvlassologit extend support to the case where the dependent variable is a binary response. In addition, rlasso implements the Chernozhukov et al. (2013) sup-score test of joint significance of the regressors that is suitable for the high-dimensional setting.