论文标题:混合效应模型的Bayes局部影响分析
Bayes Local Influence Analysis of the Mixed-effects Models
论文作者
论文导师 江其保,论文学位 硕士,论文专业 概率统计
论文单位 东南大学,点击次数 106,论文页数 42页File Size2053K
2006-02-01论文网 http://www.lw23.com/lunwen_959844097/
longitudinal data; the mixed-effects models; case deletion; influence analysis; perturbation schemes; Bayesian local influence ; Cook distance
在纵向数据分析中，人们常常采用混合效应模型。这些模型被广泛应用于生物、医学、经济、抽样设计和质量控制等领域。关于混合效应模型的统计诊断，研究成果已经很多。然而他们主要是基于频率派的，Bayes派的结果却不多见。因此本文主要考虑混合效应模型的统计诊断问题，尤其是模型的Bayes局部影响分析问题。本文根据纵向数据既包含个体又包含个体不同状态的特点，提出了两种便于合理分析数据的扰动方案，导出了模型在上述各种扰动下效应参数的Bayes局部影响度量。最后，我们用实例说明了本文给出的方法的有效性。具体地说，本文主要工作如下： (1) 第二章我们从频率派的观点出发，对模型进行了统计诊断分析，讨论了模型的杠杆值及数据删除模型，分别给出了单个个体的杠杆矩阵与删除单个个体情形时的Cook距离公式。前人一般只考虑单个观测值的情形。并通过实际数据分析，得出了高杠杆个体与数据删除模型时的强影响个体。同时我们将杠杆值分为两部分，分别讨论了模型固定效应与随机效应的边际杠杆值，得出了两种情形下的高杠杆影响个体。 (2) 我们在第三章采用分层模型思想，导出了效应参数的后验分布，并以这一分布为基础讨论了混合效应模型的Bayes局部影响分析。在扰动方式上，针对纵向数据特点下提出了个体扰动与每次观测扰动，分别用于度量单个观测值与单个个体对效应参数估计的影响，并推导出了相应的强影响个体与强影响观测的度量统计量。 (3) 最后通过实际数据分析，得出在上述各种扰动下的强影响个体与强影响观测。强影响观测结论基本与前人已有的全局影响分析结论一致，但也探测出全局影响分析中所没有发现的观测点。同时也可以看出，强影响个体与强影响观测并不存在着必然联系。某个个体的观测在某种扰动模式下对某种参数的估计来说是强影响观测，并不意味着这个个体在同种扰动下对同种参数的估计而言是强影响个体；反之，某个个体是强影响个体，也不意味着该个体的观测也能被诊断为强影响观测。
The mixed-effects models are popular in the analysis of longitudinal data. They are frequently used in biology, medicine, and economics, sampling designs and quality control procedures, and so on. In this thesis, we focused on the local influence analysis of this model. Using Bayesian method, we obtained the Bayesian local influential formulas of parameter estimates. Our result can be applied to the local influence of a particular datum as well as the data of one individual. An example is used for illustration. More precisely, our work consists of the following three parts:(1) In chapter two, we studied the statistical diagnostics of the model from a frequentist"s view-point: the leverage analysis and the case deletion model. We derived the leverage matrix of one individual which was divided into two parts : The marginal leverage of the fixed-effect and random-effect, and the Cook distance formula for the case that all the data of an individual is deleted. An example is given for illustration.(2) In chapter three, we derived the posterior distribution of the parameters based on the hierarchical model method. We proposed two types of perturbation schemes in terms of the characteristics of longitudinal data which include both individuals and individual cases. Using the posterior distribution, we analyzed the influence of a particular datum as well as the data of one individual, on the estimates of the parameters. The Bayesian local influential formulas are provided for both perturbation schemes.(3) Based on the data analysis, we got the influential individuals and the influential observations. We find that the basic result is the same to the global influence analysis. But some new cases were detected. We should emphasize that: the influential individual case and the influential individual are usually not belonged to the same individual even under the same perturbation.
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