Non-linear PLS approach in score surface

In empirical modelling, linear models are used the most frequently. This functions well in normal operations. There are situations, however, where it can be seen that the response value behaves in a non-linear manner. In such a case, it may be futile to attempt the modelling procedure in a linear way.

There are several approaches presented for these types of situations and the present work considers the use of powers of score vectors instead of merely using linear terms. The data originates from an oil refinery and suffers from a mild non-linearity. The data is modelled using PLS, polynomial PLS and non-linear PLS.

It can be seen that the non-linear extension of PLS can provide with better predictions at the extreme low and high values compared to other considered methods.