本文選題：縱向數(shù)據(jù)　切入點(diǎn)：變量選擇　出處：《山東科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在不同時刻對于不同個體或者觀測對象分別進(jìn)行若干次重復(fù)觀測,即得到了不同時刻對于不同個體的若干觀測值,這類數(shù)據(jù)我們稱其為縱向數(shù)據(jù)。平衡縱向數(shù)據(jù)是縱向數(shù)據(jù)的一類,在相同時刻對不同觀測對象進(jìn)行觀測得到的數(shù)據(jù),能反映不同個體隨時間的變化情況,在醫(yī)學(xué)、社會科學(xué)等研究中有廣泛的應(yīng)用。對此類數(shù)據(jù)進(jìn)行分析研究時,自變量的選擇是首要解決的問題。Lasso及其相關(guān)方法,在對變量壓縮提取方面有較好的效果。本文主要應(yīng)用自適應(yīng)Lasso方法及其后續(xù)改進(jìn)的自適應(yīng)彈性網(wǎng)方法的思想,通過對目標(biāo)函數(shù)添加約束來壓縮回歸系數(shù),將影響較小的自變量的回歸系數(shù)壓縮為零,解決平衡縱向數(shù)據(jù)模型的變量選擇問題。主要工作如下:第一章深入探討了平衡縱向數(shù)據(jù)的實際應(yīng)用價值,分析了研究背景及平衡縱向數(shù)據(jù)變量選擇的研究意義。第二章介紹了在變量選擇方面Lasso相關(guān)方法的應(yīng)用及發(fā)展。首先介紹了 Lasso相關(guān)方法的思想,同時介紹了最小角回歸算法,該算法能有效解決Lasso及相關(guān)方法中帶有絕對值罰函數(shù)的計算問題。最后還介紹了具有組效應(yīng)性質(zhì)的彈性網(wǎng)算法、組Lasso方法以及具有Oracle性質(zhì)的SCAD方法、自適應(yīng)Lasso方法、自適應(yīng)彈性網(wǎng)方法等。第三章和第四章分別將自適應(yīng)Lasso方法、自適應(yīng)彈性網(wǎng)方法引入平衡縱向數(shù)據(jù)模型的變量選擇中,提出平衡縱向數(shù)據(jù)自適應(yīng)Lasso變量選擇算法及平衡縱向數(shù)據(jù)自適應(yīng)彈性網(wǎng)算法。同時研究分析了兩種方法所具有的Oracle性質(zhì)和組效應(yīng)性質(zhì),并通過數(shù)值實驗分別對兩種方法進(jìn)行了驗證,分析了數(shù)值實驗結(jié)果。第五章對影響城市競爭力的主要因素進(jìn)行了分析研究。選取了 2011-2015年五年間二十座城市的二十八項指標(biāo)的統(tǒng)計數(shù)據(jù),通過對原始數(shù)據(jù)進(jìn)行加工處理,利用第三章、第四章給出的算法進(jìn)行分析,選出對城市競爭力影響較大的因素,通過實例分析驗證了算法的有效性,并分析了結(jié)果。最后在此基礎(chǔ)上對文章進(jìn)行了總結(jié),并對后續(xù)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.
【學(xué)位授予單位】：山東科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212

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