基于辅助变量的随机效应的logistic回归及其加权平均分估计

发布时间：2018-04-18 01:01

本文选题：随机效应 + 平均分方法　；参考：《闽南师范大学》2017年硕士论文

【摘要】：广义线性混合模型是一种特殊的混合模型,是对广义线性模型的一种重要扩展。在这个模型结构中,取代固定效应,线性预测量包含了具有正态分布的随机效应。随机效应logistic回归是广义线性混合模型(GLMM)的一个特殊的情况,主要应用于流行病学。本文首先介绍了随机效应logistic回归模型,提出了一个新的方法,即在平均分方法(Mean Score Method)的基础上,当出现缺失数据时,对其使用辅助变量,从而对数据进行特定中心估计,得到第一步估计量,然后对第一步估计量进行最优加权,来构造一个两步估计量。最后利用两种估计量做了模拟研究,结果表示本文提出的估计量估计恰当,最后将其应用于男婴缺陷问题中,并证明我们提出的方法在实际应用中更实用。第1章为绪论。简要叙述了随机效应logistic模型选题的背景和研究意义,以及国内外关于缺失数据处理、logistic模型和新生儿缺陷问题的研究现状。第2章介绍了随机效应的logistic回归模型,本文提出了一种特定中心的估计方法,它是在拟似然函数的基础上,对缺失数据的处理使用平均分数法的一种方法。接下来再对第一步估计量进行最优加权,来构造一个两步估计量。在第2部分的结尾给出了估计量的渐近性质。第3章是将估计量和理论值对比的模拟研究,进而对本文所提出的随机效应logistic模型的估计方法进行评价。第4章是实证分析。先介绍了本文的数据来源。并以新生儿出现缺陷数据为例,使用本文的提出的新估计方法进行估计,最后根据实证结论提出了相关建议。第5章给出本文的最后结论和不足之处。
[Abstract]:Generalized linear mixed model is a kind of special mixed model is a kind of important extension of generalized linear model. In this model structure, to replace the fixed effects, linear prediction with a normal distribution of the random effects. The random effect logistic regression is a generalized linear mixed model (GLMM) is a special the situation, mainly used in epidemiology. This paper first introduces the random effect logistic regression model, proposed a new method, namely in the average method (Mean Score Method) on the basis of when there is missing data, the use of auxiliary variables to specific estimates for the data center, the first step estimation then, the first step of the estimation of the optimal weights, to construct a two step estimator. Finally the two estimate made a simulation research, the result indicated this estimator to estimate the appropriate Applied to the problem of the baby, and proved that the proposed method is more practical in practical application. The first chapter is the introduction briefly describes the background of random effects logistic model of topics and significance, at home and abroad on the missing data, the logistic model and the lack of research in neonatal problems. The second chapter introduces the random effect the logistic regression model, this paper proposes a method to estimate the specific center, which is based on Quasi Likelihood Function, a method of using the average fraction method to handle missing data. Then the first step of the estimation of the optimal weighting, to construct a two step estimator. Theasymptotic properties estimate given in the end of the second part. The third chapter is the comparative study of simulation theory and the capacity to estimate the value of the evaluation method for the estimation of random effects logistic model and presented in this paper. The fourth chapter is the empirical analysis. First, the data source of this paper is introduced. Taking the newborn defect data as an example, we use the new estimation method proposed in this paper to estimate it. Finally, we put forward some suggestions based on the empirical conclusions. The fifth chapter gives the final conclusions and shortcomings of this paper.

【学位授予单位】：闽南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

【参考文献】