零膨胀模型及检验方法的比较研究

发布时间：2018-04-01 01:37

本文选题：计数数据　切入点：零膨胀　出处：《贵州民族大学》2017年硕士论文

【摘要】：计数数据是一类重要的数据类型,广泛存在于医学、生物和农业等领域中。当计数数据中出现零的比例超出泊松回归模型或负二项回归模型等常用计数模型的预测能力,即数据存在零膨胀现象时,若再用经典的计数模型如泊松回归模型对数据进行拟合分析就可能得到错误的统计推断结论。因此,对计数数据是否存在零膨胀现象的检验问题以及对存在零膨胀现象数据的模型选择问题研究具有重要的意义。本文基于Monte Carlo模拟方法就这两个问题进行了探讨分析,具体内容如下。第一章,就问题的研究背景、国内外研究现状以及本文的研究思路与研究内容安排做了简单的介绍。第二章,就本文研究所涉及的泊松回归模型、负二项回归模型、零膨胀泊松回归模型和零膨胀负二项回归模型及相关知识做了简单的介绍。第三章,针对计数数据是否存在零膨胀现象的检验问题,通过Monte Carlo模拟分析方法,探讨了不同零膨胀程度、不同均值和不同样本量条件下,零膨胀泊松回归模型中七种检验方法在检验功效和犯第一类错误的概率意义下的优良性,并结合实例就七种检验方法进行了简单的说明。第四章,通过Monte Carlo模拟,产生来自零膨胀泊松分布和零膨胀负二项分布的随机数,并用泊松回归模型、负二项回归模型、零膨胀泊松回归模型和零膨胀负二项回归模型对产生的随机数进行拟合分析,在不同准则下,对模型的优良性进行研究。第五章,对本文的研究结果进行了总结,并结合本文研究存在的不足,给出了后续研究的一点思考。
[Abstract]:Counting data is a kind of important data type, which widely exists in the fields of medicine, biology and agriculture. When the proportion of zero in counting data exceeds the prediction ability of common counting models such as Poisson regression model or negative binomial regression model, That is, if the classical counting model such as Poisson regression model is used to fit and analyze the data when there is zero expansion, the wrong statistical inference can be obtained. It is of great significance to examine whether there is zero expansion in the counting data and to study the model selection of the zero expansion data. This paper discusses and analyzes these two problems based on the Monte Carlo simulation method. The main contents are as follows. The first chapter introduces the background of the research, the current situation of the research at home and abroad, the research ideas and the research contents. Chapter two, the Poisson regression model, which is involved in this paper, is introduced. The negative binomial regression model, zero expansion Poisson regression model, zero expansion negative binomial regression model and related knowledge are briefly introduced. In chapter 3, the Monte Carlo simulation analysis method is used to test the existence of zero expansion phenomenon in counting data. Under the conditions of different zero expansion degree, different mean value and different sample size, seven test methods in the zero expansion Poisson regression model are discussed in the sense of test efficacy and probability of making the first kind of error. In chapter 4, through Monte Carlo simulation, random numbers from zero expansion Poisson distribution and zero expansion negative binomial distribution are generated, and Poisson regression model and negative binomial regression model are used. The zero expansion Poisson regression model and the zero expansion negative binomial regression model are used to fit and analyze the generated random numbers. Combined with the shortcomings of this study, this paper gives some thoughts on the follow-up research.
【学位授予单位】：贵州民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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