Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning
Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning
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DOI：
10.1198/jasa.2010.tm09757
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发表时间：
2010-12-01
影响因子：
3.7
通讯作者：
Schmuland, Byron
中科院分区：
文献类型：
--
作者：
Lele, Subhash R.;Nadeem, Khurram;Schmuland, Byron
广义线性混合模型 (GLMM) 的最大似然估计是一类重要的统计模型，在流行病学、医学统计学和许多其他领域有着广泛的应用，但它带来了巨大的计算困难。在本文中，我们使用数据克隆，这是一种简单的计算方法，利用贝叶斯计算的进步，特别是马尔可夫链蒙特卡罗方法，来获得这些模型中参数的最大似然估计。该方法还导致最大似然估计量的渐近方差的简单估计量。一般来说，确定混合模型中参数的可估计性是一个非常困难的问题。数据克隆提供了一种简单的图形测试，不仅可以检查整套参数是否可估计，而且也许更重要的是，可以检查参数的指定函数是否可估计。混合模型的目标之一是预测随机效应。我们建议采用频率论方法来获取随机效应的预测区间。我们通过分析过度分散的二进制数据的逻辑正态模型以及重复和空间计数数据的泊松正态模型来说明 GLMM 背景下的数据克隆。我们考虑正态正态和二元正态混合模型来展示如何使用数据克隆来研究各种参数的可估计性。我们认为，无论何时使用层次模型，在得出科学推论或做出管理决策之前都应该检查参数的可估计性。数据克隆有助于对分层模型进行此类检查。
Maximum likelihood estimation for Generalized Linear Mixed Models (GLMM), an important class of statistical models with substantial applications in epidemiology, medical statistics, and many other fields, poses significant computational difficulties. In this article, we use data cloning, a simple computational method that exploits advances in Bayesian computation, in particular the Markov Chain Monte Carlo method, to obtain maximum likelihood estimators of the parameters in these models. This method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators. Determining estimability of the parameters in a mixed model is, in general, a very difficult problem. Data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also, and perhaps more importantly, if a specified function of the parameters is estimable. One of the goals of mixed models is to predict random effects. We suggest a frequentist method to obtain prediction intervals for random effects. We illustrate data cloning in the GLMM context by analyzing the Logistic Normal model for over-dispersed binary data, and the Poisson Normal model for repeated and spatial counts data. We consider Normal Normal and Binary Normal mixture models to show how data cloning can be used to study estimability of various parameters. We contend that whenever hierarchical models are used, estimability of the parameters should be checked before drawing scientific inferences or making management decisions. Data cloning facilitates such a check on hierarchical models.