A general maximum likelihood analysis of variance components in generalized linear models
A general maximum likelihood analysis of variance components in generalized linear models
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DOI：
10.1111/j.0006-341x.1999.00117.x
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发表时间：
1999-03-01
期刊：
影响因子：
1.9
通讯作者：
Aitkin, M
中科院分区：
文献类型：
--
作者：
Aitkin, M
本文给出了具有方差分量结构的广义线性模型非参数极大似然估计的EM算法。该算法为近似的MQL和PQL分析(McGilchrist和Aisbett，1991，《生物统计学杂志》33,131-141；Breslow和Clayton，1993；《美国统计协会杂志》88，9-25；McGilchrist，1994，《皇家统计学会杂志》，B丛书，61-69；Goldstein，1995，《多水平统计模型》)和Gee分析(梁和Zeger，1986，Bitomka 73，13-22)提供了另一种分析。该算法最早是由Hinde和Wood(1987，在纵向数据分析中，110-126)提出的，是在Aitkin(1996，Statistics and Computing 6,251-262)中描述的广义线性模型中超离散随机效应模型的推广。该算法最初被推导为假设正态混合分布的高斯求积形式，但只要稍有变化就可以用于完全未知的混合分布，从而为该分布的完全非参数最大似然估计提供了一种直接的方法。这是有价值的，因为GLM参数的ML估计可能对混合分布的参数形式的规范敏感。非参数分析可以直接推广到一般的随机参数模型，对随机参数的联合分布进行全NPML估计。与随机参数的指定参数分布上的完全数值积分相比，这可以产生大量的计算节省。描述了一种在使用EM算法时获得参数估计的修正标准误差的简单方法。讨论了几个例子，涉及简单的方差分量和纵向模型，以及小区域估计。
This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation.