Park T
Department of Statistics, Hankuk University of Foreign Studies, Dongdaemun-Gu, Seoul, Korea.
Stat Med. 1993 Sep 30;12(18):1723-32. doi: 10.1002/sim.4780121807.
Liang and Zeger proposed an extension of generalized linear models to the analysis of longitudinal data. Their approach is closely related to quasi-likelihood methods and can handle both normal and non-normal outcome variables such as Poisson or binary outcomes. Their approach, however, has been applied mainly to non-normal outcome variables. This is probably due to the fact that there is a large class of multivariate linear models available for normal outcomes such as growth models and random-effects models. Furthermore, there are many iterative algorithms that yield maximum likelihood estimators (MLEs) of the model parameters. The multivariate linear model approach, based on maximum likelihood (ML) estimation, specifies the joint multivariate normal distribution of outcome variables while the approach of Liang and Zeger, based on the quasi-likelihood, specifies only the marginal distributions. In this paper, I compare the approach of Liang and Zeger and the ML approach for the multivariate normal outcomes. I show that the generalized estimating equation (GEE) reduces to the score equation only when the data do not have missing observations and the correlation is unstructured. In more general cases, however, the GEE estimation yields consistent estimators that may differ from the MLEs. That is, the GEE does not always reduce to the score equation even when the outcome variables are multivariate normal. I compare the small sample properties of the GEE estimators and the MLEs by means of a Monte Carlo simulation study.
梁和泽格提出了将广义线性模型扩展用于纵向数据分析的方法。他们的方法与拟似然方法密切相关，能够处理正态和非正态的结果变量，如泊松分布或二元结果。然而，他们的方法主要应用于非正态结果变量。这可能是因为对于正态结果存在一大类多元线性模型可用，如增长模型和随机效应模型。此外，有许多迭代算法可用于得到模型参数的最大似然估计值（MLE）。基于最大似然（ML）估计的多元线性模型方法指定了结果变量的联合多元正态分布，而基于拟似然的梁和泽格的方法仅指定了边际分布。在本文中，我比较了梁和泽格的方法与针对多元正态结果的ML方法。我表明，广义估计方程（GEE）仅在数据没有缺失观测值且相关性为非结构化时才简化为得分方程。然而，在更一般的情况下，GEE估计会产生与MLE可能不同的一致估计量。也就是说，即使结果变量是多元正态的，GEE也并不总是简化为得分方程。我通过蒙特卡罗模拟研究比较了GEE估计量和MLE的小样本性质。
