平衡纵向数据模型变量选择的相关算法研究

发布时间：2018-03-20 01:41

本文选题：纵向数据　切入点：变量选择　出处：《山东科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：在不同时刻对于不同个体或者观测对象分别进行若干次重复观测,即得到了不同时刻对于不同个体的若干观测值,这类数据我们称其为纵向数据。平衡纵向数据是纵向数据的一类,在相同时刻对不同观测对象进行观测得到的数据,能反映不同个体随时间的变化情况,在医学、社会科学等研究中有广泛的应用。对此类数据进行分析研究时,自变量的选择是首要解决的问题。Lasso及其相关方法,在对变量压缩提取方面有较好的效果。本文主要应用自适应Lasso方法及其后续改进的自适应弹性网方法的思想,通过对目标函数添加约束来压缩回归系数,将影响较小的自变量的回归系数压缩为零,解决平衡纵向数据模型的变量选择问题。主要工作如下:第一章深入探讨了平衡纵向数据的实际应用价值,分析了研究背景及平衡纵向数据变量选择的研究意义。第二章介绍了在变量选择方面Lasso相关方法的应用及发展。首先介绍了 Lasso相关方法的思想,同时介绍了最小角回归算法,该算法能有效解决Lasso及相关方法中带有绝对值罚函数的计算问题。最后还介绍了具有组效应性质的弹性网算法、组Lasso方法以及具有Oracle性质的SCAD方法、自适应Lasso方法、自适应弹性网方法等。第三章和第四章分别将自适应Lasso方法、自适应弹性网方法引入平衡纵向数据模型的变量选择中,提出平衡纵向数据自适应Lasso变量选择算法及平衡纵向数据自适应弹性网算法。同时研究分析了两种方法所具有的Oracle性质和组效应性质,并通过数值实验分别对两种方法进行了验证,分析了数值实验结果。第五章对影响城市竞争力的主要因素进行了分析研究。选取了 2011-2015年五年间二十座城市的二十八项指标的统计数据,通过对原始数据进行加工处理,利用第三章、第四章给出的算法进行分析,选出对城市竞争力影响较大的因素,通过实例分析验证了算法的有效性,并分析了结果。最后在此基础上对文章进行了总结,并对后续研究方向提出了展望。
[Abstract]:Several repeated observations are made at different times for different individuals or objects of observation, that is, a number of observations for different individuals at different times are obtained. This kind of data is called longitudinal data. Balanced longitudinal data is a kind of vertical data, and at the same time, the data from different observation objects can reflect the changes of different individuals over time, in medicine, When analyzing such data, the choice of independent variables is the most important problem. Lasso and its related methods. In this paper, the adaptive Lasso method and its subsequent improved adaptive elastic net method are used to compress the regression coefficients by adding constraints to the objective function. The regression coefficient of the less influential independent variable is reduced to zero to solve the variable selection problem of the balanced longitudinal data model. The main work is as follows: in chapter one, the practical application value of the balanced longitudinal data is discussed in depth. The research background and significance of variable selection of balanced longitudinal data are analyzed. Chapter two introduces the application and development of Lasso correlation method in variable selection. Firstly, the idea of Lasso correlation method is introduced, and the minimum angle regression algorithm is introduced. The algorithm can effectively solve the problem of computing Lasso and related methods with absolute penalty function. Finally, the elastic network algorithm with group effect, group Lasso method, SCAD method with Oracle property and adaptive Lasso method are introduced. Chapter 3 and 4th introduce adaptive Lasso method and adaptive elastic network method into variable selection of balanced longitudinal data model. The adaptive Lasso variable selection algorithm for balanced longitudinal data and the adaptive elastic network algorithm for balanced longitudinal data are proposed. The Oracle properties and group effect properties of the two methods are studied and analyzed. The two methods are verified by numerical experiments. The main factors affecting the competitiveness of cities are analyzed and studied in Chapter 5th. The statistical data of 28 indexes of 20 cities from 2011-2015 to 2015 are selected and processed by processing the original data. Based on the analysis of the algorithm in Chapter 3 and Chapter 4th, the factors that have a great impact on the competitiveness of the city are selected. The effectiveness of the algorithm is verified by an example, and the results are analyzed. The prospect of the future research is also put forward.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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