abstract Article history:Received 27 August 2010Revised 4 December 2010Accepted 8 December 2010Available online 15 December 2010 The goals of this paper are to review the most popular methods of predictor selection in regression models, toexplain why some fail when the number P of explanatory variables exceeds the number N of participants, andto discuss alternative statistical methods that can be employed in this case. We focus on penalized leastsquaresmethodsinregressionmodels,anddiscussindetailtwosuchmethodsthatarewellestablished inthestatistical literature, the LASSO and Elastic Net. We introduce bootstrap enhancements of these methods, theBE-LASSO and BE-Enet, that allow the user to attach a measure of uncertainty to each variable selected. Ourwork is motivated by a multimodal neuroimaging dataset that consists of morphometric measures (volumesat several anatomical regions of interest), white matter integrity measures from diffusion weighted data(fractional anisotropy, mean diffusivity, axial diffusivity and radial diffusivity) and clinical and demographicvariables (age, education, alcohol and drug history). In this dataset, the number P of explanatory variablesexceeds the number N of participants. We use the BE-LASSO and BE-Enet to provide the ﬁrst statisticalanalysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging andclinical predictors, including their interactions. The major novelty of this analysis is that biomarker selectionand dimension reduction are accomplished with a view towards obtaining good predictions for the outcomeof interest (i.e., the neurocognitive indices), unlike principal component analysis that are performed only onthe predictors' space independently of the outcome of interest.© 2010 Elsevier Inc. All rights reserved.
['Florentina Bunea', 'Yiyuan She', 'Hernando Ombao', 'Assawin Gongvatana', 'Kate Devlin', 'Ronald A. Cohen']
Penalized least squares regression methods and applications to neuroimaging