Negative binomial loglinear mixed models
Negative binomial loglinear mixed models
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DOI：
10.1191/1471082x03st058oa
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发表时间：
2003-10-01
影响因子：
1
通讯作者：
Hobert, JP
中科院分区：
文献类型：
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作者：
Booth, JG;Casella, G;Hobert, JP
泊松对数线性模型是解释计数变异性的常见选择。然而，在许多实际情况下，均值和方差相等的限制是不现实的。泊松分布的过度分散可以通过对混合分布进行积分来明确建模，并且使用共轭伽玛混合分布会产生负二项式对数线性模型。本文将负二项式对数线性模型扩展到相关计数的情况，其中计数之间的相关性通过在线性预测器中包含随机效应的线性组合来处理。如果我们假设随机效应向量是多元正态的，那么可以通过协方差结构的适当规范来对复杂形式的依赖性进行建模。尽管所得模型的似然函数不易处理，但可以使用 SAS 中的 NLMIXED 过程找到最大似然估计（和标准误差），或者在更复杂的示例中使用 Monte Carlo EM 算法。另一种方法是完全不指定随机效应，并尝试使用非参数最大似然来估计它们。通过几个例子来说明这些方法。
The Poisson loglinear model is a common choice for explaining variability in counts. However, in many practical circumstances the restriction that the mean and variance are equal is not realistic. Overdispersion with respect to the Poisson distribution can be modeled explicitly by integrating with respect to a mixture distribution, and use of the conjugate gamma mixing distribution leads to a negative binomial loglinear model. This paper extends the negative binomial loglinear model to the case of dependent counts, where dependence among the counts is handled by including linear combinations of random effects in the linear predictor. If we assume that the vector of random effects is multivariate normal, then complex forms of dependence can be modelled by appropriate specification of the covariance structure. Although the likelihood function for the resulting model is not tractable, maximum likelihood estimates (and standard errors) can be found using the NLMIXED procedure in SAS or, in more complicated examples, using a Monte Carlo EM algorithm. An alternate approach is to leave the random effects completely unspecified and attempt to estimate them using nonparametric maximum likelihood. The methodologies are illustrated with several examples.