Adaptive LASSO selection is a modification of LASSO selection; in adaptive LASSO selection, weights are applied to each of the parameters in forming the LASSO constraint (Zou 2006). More precisely, suppose that the response has mean zero and the regressors are scaled to have mean zero and common standard deviation. Furthermore, suppose you can find a suitable estimator of the parameters in the true model and you define a weight vector by , where . Then the adaptive LASSO regression coefficients are the solution to the constrained optimization problem
You can specify by using the INEST=suboption of the SELECTION=LASSO option in the MODEL statement. The INEST= data set has the same structure
as the OUTEST= data set that is produced by several SAS/STAT procedures, including the REG and LOGISTIC procedures. The INEST=
data set must contain all explanatory variables in the MODEL
statement. It must also contain an intercept variable named Intercept
unless you specify the NOINT option in the MODEL statement. If BY processing is used, the INEST= data set must also include
the BY variables, and there must be one observation for each BY group. If the INEST= data set also contains the _TYPE_
variable, only observations whose _TYPE_
value is PARMS
are used.
If you do not specify an INEST= data set, then PROC GLMSELECT uses the solution to the unconstrained least squares problem as the estimator . This is appropriate unless collinearity is a concern. If the regressors are collinear or nearly collinear, then Zou (2006) suggests using a ridge regression estimate to form the adaptive weights.