Generalized linear models with varying dispersion
Generalized linear models with varying dispersion
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DOI：
10.1111/j.2517-6161.1989.tb01747.x
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发表时间：
1989-09
期刊：
影响因子：
--
通讯作者：
G. Smyth
中科院分区：
文献类型：
--
作者：
G. Smyth
广义线性模型被进一步一般化，包括离散度和均值的线性预测器。它显示了如何方便的结构的广义线性模型可以延续到这个更一般的设置，分别考虑平均和分散结构。平均值和离散子模型是为此而制定的，离散子模型的因变量是平均值子模型的偏差分量。这两个子模型本质上都是广义线性模型，这一事实被用来推导出似然方程和渐近检验的简单表达式。提出了具有良好收敛性的估计算法。结果主要适用于正态分布，逆高斯分布和伽马分布，但可以通过使用准似然扩展到离散分布。所开发的方法应用于一个已知的数据集。
SUMMARY Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately. Mean and dispersion submodels are formulated for this, the dependent variable for the dispersion submodel being the deviance components of the mean submodel. The fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests. Estimation algorithms are proposed which have good convergence properties. The results apply mainly to the normal, inverse Gaussian and gamma distributions but can be extended to discrete distributions by using quasi-likelihoods. The methods developed are applied to a well-known data set.