Variable selection and importance in presence of high collinearity: an application to the prediction of lean body mass from multi-frequency bioelectrical impedance

In prediction problems both response and covariates may have high correlation with a second group of influential regressors, that can be considered as background variables. An important challenge is to perform variable selection and importance assessment among the covariates in the presence of these variables. A clinical example is the prediction of the lean body mass (response) from bioimpedance (covariates), where anthropometric measures play the role of background variables. We introduce a reduced dataset in which the variables are defined as the residuals with respect to the background, and perform variable selection and importance assessment both in linear and random forest models. Using a clinical dataset of multi-frequency bioimpedance, we show the effectiveness of this method to select the most relevant predictors of the lean body mass beyond anthropometry.