کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1150027 957910 2007 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence rate of MLE in generalized linear and nonlinear mixed-effects models: Theory and applications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Convergence rate of MLE in generalized linear and nonlinear mixed-effects models: Theory and applications
چکیده انگلیسی

Generalized linear and nonlinear mixed-effects models are used extensively in the study of repeated measurements and longitudinal data analysis. Convergence rates of maximum likelihood estimates (MLEs) differ from parameter to parameter, which is not well explained in the literature. We consider the convergence rates of the MLEs for three different 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; (3) n remains finite while p   tends to infinity. In the three cases above, the MLE may have different convergence rates. In case (1), as we can expect, the MLE of all parameters are n-consistent under some regularity conditions; in case (2), some parameters could be 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 one example and through presenting the exact convergence rates of some “approximate” MLEs such as PQL, CGEE2, etc. It is shown that the MLE for some parameters and some “approximate” MLEs may be N-consistent, here N=npN=np is the total sample size. Also our results show that the MLE of some parameters maybe asymptotically independent of some other parameters.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 137, Issue 6, 1 June 2007, Pages 1787–1804
نویسندگان
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