Extra‐Poisson Variation in Log‐Linear Models
Extra‐Poisson Variation in Log‐Linear Models
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DOI：
10.2307/2347661
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发表时间：
1984-03
期刊：
影响因子：
--
通讯作者：
N. Breslow
中科院分区：
文献类型：
--
作者：
N. Breslow
Pocock et al. (1981) proposed a large sample solution to the problem of fitting regression models to tables of rates when the residual variation is substantially in excess of that expected from Poisson sampling theory. Operationally, their method consists of making iterated weighted least squares fits to approximately normally distributed dependent variables consisting of the observed rates or their logarithms. The variance of each observation is assumed equal to the sampling variance of the (transformed) rate plus an unknown constant representing extraneous sources of variability. Williams (1982) subsequently introduced a similar scheme for handling extra-binomial variation in linear-logistic models whether fitted by weighted least squares or maximum likelihood. This note adapts his procedure to the Poisson case and compares results obtained by different methods with several sets of data. The primary goal is to demonstrate the utility of such procedures and to show that they may be readily implemented using standard software.
