一般计数资料Poisson分布模型回归分析
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摘要
本文目的是介绍一般计数资料Poisson分布模型回归分析。首先,介绍一般计数资料及其Poisson分布模型构建原理,包括"一般计数资料Poisson分布回归模型的形式"和"一般计数资料Poisson分布回归模型的求解";其次,介绍"一般计数资料Poisson分布回归模型的SAS实现",包括"创建SAS数据集""求出因变量Y的均值和方差""检验因变量是否存在过离散现象""对过离散进行校正"和"基于全部自变量对因变量Y构建多重Poisson分布回归模型"。本文结果提示,在"过离散"不十分严重的情况下,通过在GENMOD过程的"model语句"中增加选项"dist=poisson"和"scale=deviance",可以较好地校正"过离散"导致的不良后果。
The purpose of this paper was to introduce the regression analysis of the Poisson distribution model for the general count data. Firstly,the concepts of the general count data and the building principle of the Poisson distribution regression model were introduced,which included the following two aspects:(1) the form of the Poisson distribution regression model of count data;(2) the solution for the model mentioned before. Secondly,the SAS realization of the Poisson distribution regression model of count data was presented. The contents were as follows:(1)creating SAS data set;(2)calculating the arithmetic mean and variance of the dependent variable Y;(3)checking whether there was the overdispersion in the dependent variable Y;(4)adjusting the overdispersion;(5)building a multiple Poisson distribution regression model for the dependent variable Y based on all independent variables. The results of the article showed that,under the situation of not severe overdispersion,the harmful results came from the overdispersion could be adjusted preferably through the following measures,such as using options of " dist = poisson" and " scale = deviance" in the model statement in the GENMOD procedure in SAS software.
The purpose of this paper was to introduce the regression analysis of the Poisson distribution model for the general count data. Firstly,the concepts of the general count data and the building principle of the Poisson distribution regression model were introduced,which included the following two aspects:(1) the form of the Poisson distribution regression model of count data;(2) the solution for the model mentioned before. Secondly,the SAS realization of the Poisson distribution regression model of count data was presented. The contents were as follows:(1)creating SAS data set;(2)calculating the arithmetic mean and variance of the dependent variable Y;(3)checking whether there was the overdispersion in the dependent variable Y;(4)adjusting the overdispersion;(5)building a multiple Poisson distribution regression model for the dependent variable Y based on all independent variables. The results of the article showed that,under the situation of not severe overdispersion,the harmful results came from the overdispersion could be adjusted preferably through the following measures,such as using options of " dist = poisson" and " scale = deviance" in the model statement in the GENMOD procedure in SAS software.
引文
[1]茆诗松.统计手册[M].北京:科学出版社,2003:1004-1007.
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[3]胡良平.多重线性回归分析的核心内容与关键技术概述[J].四川精神卫生,2018,31(1):1-6.
[4]谷恒明,胡良平.基于经典统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):7-11.
[5]谷恒明,胡良平.基于贝叶斯统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):12-14.
[6]谷恒明,胡良平.基于机器学习统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):15-18.
[7]柳青.中国医学统计百科全书——多元统计分册[M].北京:人民卫生出版社,2004:231-233.
[2]胡良平.面向问题的统计学——(2)多因素设计与线性模型分析[M].北京:人民卫生出版社,2012:283-290.
[3]胡良平.多重线性回归分析的核心内容与关键技术概述[J].四川精神卫生,2018,31(1):1-6.
[4]谷恒明,胡良平.基于经典统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):7-11.
[5]谷恒明,胡良平.基于贝叶斯统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):12-14.
[6]谷恒明,胡良平.基于机器学习统计思想实现多重线性回归分析[J].四川精神卫生,2018,31(1):15-18.
[7]柳青.中国医学统计百科全书——多元统计分册[M].北京:人民卫生出版社,2004:231-233.