臺灣博碩士論文加值系統

日常生活中，我們每年例行性的健康檢查，或是在投資時都會看各家公司歷年每季的財務報表，再者像是在從事生產工作時，關注每個系列產品的每批生產的品質水準等等，都是屬於群集長期追蹤資料(clustered longitudinal data)。而這種資料型態在群集跟群集之間是獨立的，且群集內所考量的因子間具有縱相關，每個因子還有重複觀測的特性，重複觀測是因為時間的推移，所以也具有相關性。


早在 1992 年，由 Liang, Zeger 和 Qaqishy 提出的廣義估計方程式(generalized estimating equations,GEE)即應用在此類型的資料分析。後來發現這類型的資料容易有缺失值，讓我們難以精確地估計模型參數， Robins、Rtnitzky 和Zhao 在 1995 年發表的加權廣義估計方程式(weighted generalized estimating equa- tions,WGEE) ，即可用來處理在此類型的資料分析。


在本論文中，我們將應用加權廣義估計方程式，利用「泰勒展開式」、「擾動法」、「拔靴法」去進行資料有缺失值時的參數估計，並比較其在模型選擇上的優劣，最後使用國民健康檢查的實例作為上述方法在實務上的驗證。
關鍵字：cluster; longitudinal; MLIC; WGEE

In our life, we routinely conduct health examination every year, or we read financial statements of companies at each quarter when investing. Another one, when working in production, we pay attention to the quality of production of every batch of each series, etc.. All of these are belong to clustered longitudinal data. And this data type is independent between the cluster and the cluster, and there is a vertical correlation between the factors considered in the cluster. The factors also have the characteristics of repeated observations, and the repeated observations are due to the passage of time, so they are also relevant.
As early as 1992, the generalized estimating equation (GEE) proposed by Liang, Zeger and Qaqishy, and are applied to data analysis of this type. Later ,they discov- ered this data type that is easy to have missing values, which makes it difficult to accurately estimate parameters of models. Robins, Rtnitzky and Zhao’s published weighted generalized estimating equation (WGEE) in 1995, it can be used to analysis the data type with missing values.
In this paper, we will apply weighted generalized estimating equations (WGEE) by ”Taylor’s expansion”, ”Perturbation method” and ”Bootstrap Method” to esti- mate the parameters when the data has missing values, and compare the advantages and disadvantages of the model selection. Finally, we use the data of routinely health examination by old human as the verification of the method above.


Keywords：cluster; longitudinal; MLIC; WGEE

目錄





















第一章 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7



第二章 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . . . . 9



2.1 符號定義 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 廣義估計方程式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 加權廣義估計方程式 . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

第三章 三種模型選擇指標之估計法 . . . . . . . . . . . . . . . . . . 19

3.1 泰勒展開式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 資料擾動法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 拔靴法(bootstrap) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

第四章 模擬研究 . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 群集間有相關性之連續型長期追蹤資料 . . . . . . . . . . . . . . . . . 25

4.2 群集間有相關性之二元型長期追蹤資料 . . . . . . . . . . . . . . . . . 30

4.3 群集間有相關性之長期追蹤資料之模擬結論 . . . . . . . . . . . . . . 34

第五章 實例分析 . . . . . . . . . . . . . . . . . . . . . . . . . . 35

第六章 結論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

















文獻參考 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

附錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

文獻參考





Liang,K.Y., Zeger, S. L. and Qaqish, B.(1992)”Multivariate Regression Anal- yses for Categorical Data”(with discussion), Journal of the Royal Statistical Society, Ser.B,54,3-40


Robins,J.M.,Rotnitzky,A.,and Zhao.L.P.(1995). Analysis of semiparametric re- gression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association, 90, 106-121.


Liang,K.Y.and Zeger, S.L.(1986)”Longitudinal Data Analysis Using General- ized Linear Models,” Biometrika 73, 13-22


Shen, C.W. and Chen, Y. H.(2012), Model selection for generalized estimating equations accommodating dropout missingness. Biometrics, 68(4), 1046-1054.


Ye,J.(1998), On Measuring and Correcting the Effects of Data Mining and Model Selection. Journal of the American Statistical Association, 93(44), 120- 131.


Michael Sherman,Saskia le Cessie (1997), A comparison between bootstrap methods and generalized estimating equations for correlated outcomes in gen- eralized linear models. Communications in Statistics, 26(3), 901-925.