Variable selection in multi-block regression

• MB-PLS and SO-PLS coupled with SR, VIP and Forward Selection are discussed for one sensory, one spectroscopic and a number of simulated data sets.
• In the sensory data set, if the aim is to point out the most relevant variables, SO-PLS + VIP or SO-PLS + SR are the suggested approaches.
• SO-PLS + VIP appears the most efficient approach in giving the chemical interpretation of the spectroscopic (Raman) system.

The focus of the present paper is to propose and discuss different procedures for performing variable selection in a multi-block regression context. In particular, the focus is on two multi-block regression methods: Multi-Block Partial Least Squares (MB-PLS) and Sequential and Orthogonalized Partial Least Squares (SO-PLS) regression. A small simulation study for regular PLS regression was conducted in order to select the most promising methods to investigate further in the multi-block context. The combinations of three variable selection methods with MB-PLS and SO-PLS are examined in detail. These methods are Variable Importance in Projection (VIP) Selectivity Ratio (SR) and forward selection. In this paper we focus on both prediction ability and interpretation. The different approaches are tested on three types of data: one sensory data set, one spectroscopic (Raman) data set and a number of simulated multi-block data sets.