Developing Tools to Evaluate Non-linear Mixed Effect Models: 20 Years on the npde Adventure.

This article revisits 20 years of our work in developing evaluation tools adapted to non-linear mixed effect models. These hierarchical models involve a large number of assumptions concerning the structural evolution of the outcomes, the link between different outcomes, the variabilities in the parameters and model evaluation aims at assessing these various components, both to help guide the model building and to communicate on model adequacy for a given purpose. During our career, we have developed and extended simulation-based evaluation tools called normalised prediction discrepancies (npd) and normalised prediction distribution errors (npde), providing informative diagnostics through graphs and tests.