Non-linear mixed-eﬀects models
In many applications, particularly in the biological sciences, the time course of a continuous response for an individual may be characterized by a function that is non-linear in one or more parameters, where an “individual” may be a human subject, an animal, a plant, an agricultural plot, a laboratory sample, or other observational unit. The non-linear function may be chosen on empirical grounds for its ability to represent faithfully the apparent individual-speciﬁc response-time relationship. For example, the logistic growth model, discussed in Section 5.2.1, is often adopted for this reason to describe the S shape, typical of relationships between continuous measures of growth and time on a given plant or plot. Alternatively, a non-linear model for individual behavior may arise from theoretical,
mechanistic considerations that are of central scientiﬁc interest. In pharmacokinetics, as we demonstrate in Section 5.2.2, non-linear models for drug concentrations achieved over time following administration of a drug are derived from representing the body as a system of “compartments,” embodying assumptions on how processes of drug absorption, distribution, and elimination take place within a subject.