Fitting Nonlinear Mixed Effects Models by Laplace Approximation

Laura Jean Piersol
Ph.D., 2000
Advisor: Robert Jennrich

This dissertation focuses on approximate methods of estimating parameters of nonlinear mixed effects models. Five methods of estimation are compared, including Direct Least Squares, a method attributed to Lindstrom and Bates, a method attributed to Beal and Sheiner, and two forms of the Laplace Approximation. An algorithm for obtaining Laplace estimates using numerical derivatives and a quasi-Newton approximation to the Hessian of the Laplace log-likelihood is provided. Theoretical results are given. A number of examples are used to compare the performance of the methods. With the exception of the Laplace Method, the estimates using the approximate methods exhibit bias for some of the examples. An overall summary using mean relative errors of the performance of the methods on many examples is given.