Abstract
Within the context of Partial Least Squares (PLS) regression, Variable Importance in the Projection (VIP) index is extensively used to highlight the relative importance of a given variable in predicting the response. Very often, it is used as a means to select relevant variables by retaining those variables with a VIP value greater than one. As a starting point of this paper, the VIP index is expressed in matrix notation and extended to (i) a subset of variables instead of one variable at a time and (ii) the framework of Principal Component Analysis (PCA). In a subsequent stage, it is proposed to assess the significance of the VIP values of a given subset of variables based on a permutation test. A fast variable selection procedure is then proposed, taking advantage of the first extension. The theory is illustrated using multiblock spectral and omics data.
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