Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection

In multivariate PLS (partial least square projection to latent structures) and PC (principal component) models with many variables, plots and lists of b loadings, coefficients, VIPs, etc. become messy and results are difficult to interpret. There is then a strong temptation to reduce the variables to a smaller, more manageable number. This reduction of variables, however, often removes information, makes the interpretation misleading and seriously increases the risk of spurious models.