Reliable estimation of generalized linear mixed models using adaptive quadrature
Reliable estimation of generalized linear mixed models using adaptive quadrature
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DOI：
10.1177/1536867x0200200101
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发表时间：
2002-03-01
期刊：
影响因子：
4.8
通讯作者：
Pickles, Andrew
中科院分区：
文献类型：
--
作者：
Rabe-Hesketh, Sophia;Skrondal, Anders;Pickles, Andrew
广义线性混合模型或多水平回归模型已经变得越来越流行。已经提出了几种方法来估计这样的模型。然而，到目前为止，没有一种方法，可以假设在所有情况下，在参数恢复和计算效率方面都很好地工作。Stata的xt命令用于两级广义线性混合模型（例如，xtlogit）采用Gauss-Hermite求积来评估和最大化边际对数似然。该方法通常工作得很好，并且通常比常见的竞争者（如MQL和PQL）更好，但在某些情况下，正交性能较差。自适应正交已被建议克服这些问题，在两个级别的情况下。我们最近在gllamm中实现了这种方法的多级版本，gllamm是一个适合包括多级广义线性混合模型在内的一大类多级潜变量模型的程序。据我们所知，这是第一次，自适应正交已被提出的多级模型。我们表明，自适应正交工程以及普通正交失败的问题。此外，即使在普通正交工作时，自适应正交通常在计算上更有效，因为它需要更少的正交点来实现相同的精度。
Generalized linear mixed models or multilevel regression models have become increasingly popular. Several methods have been proposed for estimating such models. However, to date there is no single method that can be assumed to work well in all circumstances in terms of both parameter recovery and computational efficiency. Stata's xt commands for two-level generalized linear mixed models (e.g., xtlogit) employ Gauss-Hermite quadrature to evaluate and maximize the marginal log likelihood. The method generally works very well, and often better than common contenders such as MQL and PQL, but there are cases where quadrature performs poorly. Adaptive quadrature has been suggested to overcome these problems in the two-level case. We have recently implemented a multilevel version of this method in gllamm, a program that fits a large class of multilevel latent variable models including multilevel generalized linear mixed models. As far as we know, this is the first time that adaptive quadrature has been proposed for multilevel models. We show that adaptive quadrature works well in problems where ordinary quadrature fails. Furthermore, even when ordinary quadrature works, adaptive quadrature is often computationally more efficient since it requires fewer quadrature points to achieve the same precision.