I have been doing what you seem to refer to as non linear modelling in transport demand analysis since 1975. More formally, the issue raised is that of the proper form of variables (and sometimes of functions) and I have adressed it with Box-Cox transformations, both direct and indirect, as you will see from three enclosed documents pertaining both to models of levels (generalization of classical regression) and logit models (discrete or aggregate) and to various algorithms to estimate the parameters and derive meaningful statistics from them. If you have questions after looking at those (available on ResearchGate in any case, but enclosed for convenience), let me know.