JSM 2005 Online Program

Abstract #304471

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	484
Type:	Contributed
Date/Time:	Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor:	IMS
Abstract - #304471
Title:	Convergence Rate of MLE in Generalized Linear and Nonlinear Mixed-effects Models
Author(s):	Nie Lei*+
Companies:	University of Maryland Baltimore County
Address:	1000 Hilltop CIrcle, Baltimore, MD, 21250, United States
Keywords:	generalized linear and nonlinear models ; Convergence rate; ; Laplace's approximation; ; MLE
Abstract:	Generalized linear and nonlinear mixed-effects models are used extensively in the study of repeated measurements and longitudinal data. Convergence rates of MLE differ from parameter to parameter, which is not well explained in the literature. We consider the convergence rates of the MLEs for three cases: (1) the number of subjects (clusters) n tends to infinity while the number of measurements per subject p remains finite; (2) both n and p tend to infinity; and (3) n remains finite while p tends to infinity. In the three cases above, MLE may have different convergence rates. In case (1), as we can expect, MLE of all parameters are root n-consistent under some regularity conditions; in case (2), some parameters could be root np-consistent. These rates of convergence have a crucial impact on both experimental design and data analysis. Limited simulations were performed to examine the theoretical results. We illustrate applications of our results through an example and presenting the exact convergence rates of some "approximate" MLE, such as PQL and CGEE2.

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