Variable Selection With Prior Information for Generalized Linear Models via the Prior LASSO Method

Abstract

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This article proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the least angle regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real dataset from a genome-wide association study. Supplementary materials for this article are available online.

• Asymptotic efficiency
• Oracle inequalities
• Solution path
• Weak oracle property.