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Variable selection in monotone single‐index models via the adaptive LASSO
Author(s) -
Foster Jared C.,
Taylor Jeremy M.G.,
Nan Bin
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5834
Subject(s) - lasso (programming language) , index (typography) , selection (genetic algorithm) , monotone polygon , variable (mathematics) , feature selection , statistics , computer science , econometrics , mathematics , artificial intelligence , mathematical analysis , geometry , world wide web
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. 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 unknown 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 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 for the treatment of a critical illness in the intensive care unit. Copyright © 2013 John Wiley & Sons, Ltd.