An improved method for the computation of maximum likeliood estimates for multinomial overdispersion models

作     者：Neerchal, NK Morel, JG 

作者机构：Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA P&G Pharmaceut Inc Biometr & Stat Sci Dept Mason OH 45040 USA 

出 版 物：《COMPUTATIONAL STATISTICS & DATA ANALYSIS》 (计算统计学与数据分析)

年 卷 期：2005年第49卷第1期

页      面：33-43页

核心收录：

学科分类：08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：mixture of multinomial distributions Fisher scoring algorithm Dirichlet-multinomial distribution beta-binomial distribution 

摘      要：In this article, we consider the maximum likelihood estimation of two commonly used overdispersion models, namely, the Dirichlet-multinomial distribution (DM), due to Mosimann (Biometrika 49 (1962) 65), and a finite mixture distribution (FM) proposed by Morel and Nagaraj (Biometrika 80 (1993) 363), and Neerchal and Morel (J. Amer. Statist. Assoc. 93 (1998) 1078). These models have been successfully used in the literature for modeling overdispersion in multinomial data. Maximum likelihood estimation of the parameters of these models using the classical Fisher scoring method poses certain computational challenges. In the case of DM, the challenges are overcome by noting that the Fisher information matrix can be computed using the beta-binomial distribution (BB), which is the univariate version of DIM. On the other hand, in the case of FM, an approximation theorem call be used to obtain a two-stage procedure for computing the maximum likelihood estimates. Simulation results show that the two-stage procedure is faster without loosing any accuracy. (C) 2004 Elsevier B.V. All rights reserved.