Variable Selection in Monotone Single-Index Models via the Adaptive Lasso

• Activity Number: 570
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Jared Foster*+ and Jeremy Michael George Taylor and Bin Nan
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: variable selection ; isotonic regression ; LASSO ; single-index models ; kernel estimator

Abstract

We consider the problem of variable selection for monotone single-index models. A single-index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates. Assuming monotonicity of the unknown function is often reasonable, and allows for more straightforward inference. We present an adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome Y. Monotone function estimates are achieved using the pooled adjacent violators algorithm, followed by kernel regression. In the iterative estimation process, a linear approximation to the link function is used, therefore reducing the situation to that of linear regression, and allowing for the use of standard LASSO algorithms, such as coordinate descent. Results of a simulation study indicate that the proposed methods perform quite well under a variety of circumstances, and that an assumption of monotonicity, when appropriate, noticeably improves performance. The proposed methods are applied to data from a randomized clinical trial.