The main features of the QUANTSELECT procedure are as follows:
supports the following model specifications:
interaction (crossed) effects and nested effects
constructed effects such as regression splines
hierarchy among effects
partitioning of data into training, validation, and testing roles
provides the following selection controls:
multiple methods for effect selection
selection for quantile process and single quantile levels
selection of individual or grouped effects
selection based on a variety of selection criteria
stopping rules based on a variety of model evaluation criteria
produces the following display and output:
graphical representation of the selection process
output data sets that contain predicted values and residuals
an output data set that contains the design matrix
macro variables that contain selected effects
The QUANTSELECT procedure supports the following effect selection methods. These methods are explained in detail in the section Effect Selection Methods.
Forward selection starts with no effects or with forced-in effects in the model and adds more effects.
Backward elimination starts with all effects in the model and deletes effects.
Stepwise regression is similar to the forward selection method except that effects already in the model do not necessarily stay there.
LASSO regression adds and deletes effects based on a constrained version of estimated check risk where the L1-norm of regression coefficients is penalized (Tibshirani, 1996; Belloni and Chernozhukov, 2011). Adaptive LASSO (Zou, 2006; Wu and Liu, 2009) is implemented as a special case of LASSO methods where the L1-norm of certain weighted regression coefficients is penalized. See the discussion in the section LASSO Method (LASSO) for additional details. The QUANTSELECT procedure uses LASSO methods only to determine the adding and dropping covariate effects at a step; a post-penalized model that is associated with the step is refitted without penalty, and the selection criteria and the parameter estimates are from the post-penalized model.
The QUANTSELECT procedure is intended primarily as an effect selection procedure and does not include regression diagnostics and hypothesis testing. The intention is that you use the QUANTSELECT procedure to select a model or a set of models, where each model contains a set of selected effects, and then you can further investigate these models by using PROC QUANTREG or other analytic tools.