Nonlinear mixed-effects models

Stata’s new menl command fits nonlinear mixed-effects models, also known as nonlinear multilevel models and nonlinear hierarchical models. These models can be thought of two ways. You can think of them as nonlinear models containing random effects. Or you can think of them as linear mixed-effects models in which some or all fixed and random effects enter nonlinearly. However you think of them, the overall error distribution is assumed to be Gaussian.

These models are popular because some problems are not, says their science, linear in the parameters. These models are popular in population pharmacokinetics, bioassays, and studies of biological and agricultural growth processes.

For example, nonlinear mixed-effects models have been used to model

  • drug absorption in the body,
  • intensity of earthquakes, and
  • growth of plants.