纵向数据半参数混合效应模型的经验似然估计

发布时间：2018-03-26 02:50

本文选题：半参数广义线性混合效应模型　切入点：纵向数据　出处：《浙江财经大学》2017年硕士论文

【摘要】：纵向数据指的是对每个受试单位在不同时间点上重复测量而收集到的数据,该数据内部往往存在相依性。当对纵向数据进行建模时,必须将组内相依性考虑在内,否则会降低推断的效。因此,在分析纵向数据时,包含有随机效应的混合效应模型是常用的模型之一。虽然混合效应模型可以用来分析纵向数据,且具有很强的解释能力,但过度地假设响应变量和协变量之间的线性关系,容易导致兴趣参数不相合的估计。因此,在混合效应模型中加入半参数分量,从而形成半参数混合效应模型(Partial Linear Mixed Effects Model,简称PLMM)。PLMM中既包含固定效应和随机效应,又包含参数部分和非参数部分,充分利用了数据的信息,具有良好的适用性和灵活性。因此,该模型被广泛应用于纵向数据的分析中,对基于纵向数据的PLMM的统计推断的研究具有一定的理论意义和实用价值。具体地,论文主要包括如下几个部分:第一章首先简单介绍了纵向数据的背景以及研究意义,然后论述了模型的背景及估计方法,最后介绍了经验似然方法的发展状况及推断过程;第二章论述了半参数混合效应模型的参数估计问题,利用广义经验似然(Generalized Empirical Likelihood,简称GEL)方法对该模型进行了参数估计,得到了参数分量、非参数分量以及方差分量的估计量,并在一定条件下证明了估计量的大样本性质。第三章讨论了半参数广义线性混合效应模型(Generalized Partial Linear Mixed Effects Model,简称GPLMM)参数估计问题,利用GEL方法对该模型进行了参数估计,得到了参数分量、非参数分量以及方差分量的估计量,并在一定条件下证明了估计量的大样本性质。第四章进行了实证分析,将上述研究方法应用到小孩呼吸道感染的医学实例中去,用于说明所提出的方法的有效性。第五章对本文的研究成果、在研究过程中的体会以及值得继续研究的地方做了总结。本文的创新之处主要有以下两个方面:(1)首次利用GEL方法对GPLMM的统计推断问题进行研究,使得该方法的应用范围得到了扩展。(2)鉴于纵向数据具有组内相依性的特点,在构造参数的统计量时,加入了组内协方差阵,从而得到参数的广义经验对数似然比函数。由于将数据的组内相依性考虑在内,模型统计推断的有效性得到了改善。
[Abstract]:Longitudinal data refers to data collected from repeated measurements at different points in time for each of the subjects, which often have internal dependencies. When modeling longitudinal data, it is important to take intra-group dependencies into account. Otherwise, the effect of inference will be reduced. Therefore, when analyzing longitudinal data, a mixed effect model with random effects is one of the commonly used models. Although the mixed effect model can be used to analyze longitudinal data, it has a strong explanatory power. However, the linear relationship between response variables and covariables is assumed excessively, which easily leads to the estimation of inconsistent parameters of interest. Therefore, a semi-parametric component is added to the mixed effect model. Thus, the partial Linear Mixed Effects Model (PLMM).PLMM), which contains both fixed and random effects, parametric and non-parametric effects, makes full use of the information of the data and has good applicability and flexibility. The model is widely used in the analysis of longitudinal data. The research on statistical inference of PLMM based on longitudinal data has certain theoretical significance and practical value. The thesis mainly includes the following parts: the first chapter briefly introduces the background of longitudinal data and its research significance, then discusses the background and estimation methods of the model, and finally introduces the development and inference process of empirical likelihood method; In the second chapter, the parameter estimation problem of semi-parametric mixed effect model is discussed. The generalized empirical likelihood generalized Empirical Likelihood (Gel) method is used to estimate the parameters of the model, and the estimators of parametric component, nonparametric component and variance component are obtained. In chapter 3, the generalized Partial Linear Mixed Effects model (GPLMMMM) parameter estimation problem is discussed, and the GEL method is used to estimate the parameters of the model. The estimators of parametric component, nonparametric component and variance component are obtained, and the properties of large sample of estimator are proved under certain conditions. The above research method is applied to the medical example of respiratory tract infection in children to illustrate the effectiveness of the proposed method. The main innovations of this paper are the following two aspects: 1) the GEL method is used to study the statistical inference of GPLMM for the first time. In view of the dependence of the longitudinal data within the group, the covariance matrix within the group is added in the construction of the statistics of the parameters. The generalized empirical logarithmic likelihood ratio function of parameters is obtained, and the validity of statistical inference of the model is improved by taking into account the intra-group dependence of the data.
【学位授予单位】：浙江财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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