Variable importance index based on the partial least squares and boxplot cutoff threshold for variable selection

Abstract

The variable importance in projection or VIP index obtained by the partial least squares regression (PLS-R) has become a crucial measurement of each predictor to relieve a problem of measuring multiple variables per sample. It has been applied to classification task although it is designed for regression. The new variable importance index combining concept of PLS-R and boxplot cutoff threshold, VIIC-BCT, was here particularly presented for classification of high dimensional data. The proposed VIIC-BCT was compared to the traditional VIP index (VIP-1) and the modified VIP index with boxplot cutoff threshold (VIP-BCT) thru simulation. The four parameters, percentage of the number of relevant variables (Prel), magnitude of mean difference of relevant variables between two classes (Mdif), degree of correlation between relevant variables (Σ) and the sample size (n), were specified to generate the specific 108 situations. The result indicated the VIIC-BCT shows the best performance in the particularly complicated circumstance.