Statistics, Department of


Date of this Version


Document Type



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
Copyright (c) 2009 Meijian Zhou


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.