Selection of a penalty parameter is fundamental to lasso analysis. Using a small penalty may include too many variables. Using a large penalty may omit potentially important variables.
Lasso estimation already provides several penalty-selection methods, including cross-validation, adaptive, and plugin. You can now use the Bayesian information criterion (BIC) to select the penalty parameter after lasso for prediction and lasso for inference by specifying the selection(bic) option. Also, the new postestimation command bicplot plots the BIC values as a function of a penalty parameter after fitting a lasso model. This provides a convenient graphical representation for the value of the penalty parameter that minimizes the BIC function.