## The Nonlinear Mixed Effects Model with a Smooth Random Effects Density

Marie Davidian, A. Ronald Gallant

*Biometrika*, Vol. 80, No. 3. (Sep., 1993), pp. 475-488.

### Abstract

The fixed parameters of the nonlinear mixed effects model and the
density of the random effects are estimated jointly by maximum
likelihood. The density of the random effects is assumed to be smooth
but is otherwise unrestricted. The method uses a series expansion that
follows from the smoothness assumption to represent the density and
quadrature to compute the likelihood. Standard algorithms are used for
optimization. Empirical Bayes estimates of random coefficients are
obtained by computing posterior modes. The method is applied to data
from pharmacokinetics, and properties of the method are investigated
by application to simulated data.
**Keywords: **Maximum likelihood, Nonlinear mixed effects model,
Nonparametric, Pharmacokinetics