Fully Exponential Laplace Approximation EM Algorithm for Nonlinear Mixed Effects Models

Authors

Meijian Zhou, University of Nebraska-LincolnFollow

First Advisor

Anne M. Parkhurst

Date of this Version

12-2009

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Statistics

Under the supervision of Professor Anne M. Parkhurst

Lincoln, Nebraska, December 2009

Comments

Copyright 2009, Meijian Zhou. Used by permission

Abstract

Nonlinear mixed effects models provide a flexible and powerful platform for the analysis of clustered data that arise in numerous fields, such as pharmacology, biology, agriculture, forestry, and economics. This dissertation focuses on fitting parametric nonlinear mixed effects models with single- and multi-level random effects. A new, efficient, and accurate method that gives an error of order O(1/n²), fully exponential Laplace approximation EM algorithm (FELA-EM), for obtaining restricted maximum likelihood (REML) estimates in nonlinear mixed effects models is developed. Sample codes for implementing FELA-EM algorithm in R are given. Simulation studies have been conducted to evaluate the accuracy of the new approach and compare it with the Laplace approximation as well as four different linearization methods for fitting nonlinear mixed effects models with single-level and two-crossed-level random effects. Of all approximations considered in the thesis, FELA-EM algorithm is the only one that gives unbiased or close-to-unbiased (%Bias < 1%) estimates for both the fixed effects and variance-covariance parameters. Finally, FELA-EM algorithm is applied to a real dataset to model feeding pigs’ body temperature and a unified strategy for building crossed and nested nonlinear mixed effects models with treatments and covariates is provided.

Advisor: Anne M. Parkhurst