臺灣博碩士論文加值系統

在許多科學的追蹤研究中往往會選定一組固定樣本，針對樣本中每一叢集在不同時間點收集某些應變項及解釋變項之觀測值，而得到所謂的「多變量長期追蹤叢聚資料」。在這些研究中，人們常有興趣發展適當多變量迴歸模型以探討反應變項及解釋變項之間的相互關係，並將多變項之間的相關性考慮進去。
在本篇論文中，我們提出一種多變量迴歸模型來分析多變量二元長期追蹤叢聚資料。此模型中假設二元應變項是利用具有標準常態分佈的潛在變數，經由門檻概念所產生，其中潛在變數之期望值是由二元應變項邊際迴歸所決定。根據資料的叢聚結構，本模型進一步將潛在變數的隨機成份分解成若干個隨機效應項，以便探討單應變項資料在叢集內相關性的來源。藉由建造任兩個應變項潛在變數間相關係數的迴歸模型，本模型也可以探討多應變項間的相關性的來源。使用這種潛在變數方法，可以很容易造出操作性變異矩陣並利用廣義估計方程式方法進行參數估計。
為說明所提模型的效用，我們分析了以家庭為抽樣單位在國內長期追蹤所收集到的代謝異常資料。藉由探討代謝異常指標的危險因子及指標內與指標間相關性來源，希望能為流行病研究專家提供一些有用的資訊。

In many scientific follow-up studies, repeated observations of several response variables, along with other covariate variables, are taken from a fixed sample of clusters, resulting in multivariate longitudinal clustered data. It is often of interest in these studies to develop appropriate multivariate regression models for investigating the relationships between the
response variables and the covariates while taking into account the association among multiple responses.
In the thesis, we propose a multivariate regression model for analyzing longitudinal clustered data of multivariate binary responses. Normally distributed latent variables with unit variance are assumed to generate the observed binary response variables via a common threshold. The expectations of the latent variables are determined from the marginal regression of the observed binary variables. Based on the clustering structure for the data at hand, the random error of the latent variable is further decomposed into several random effect terms to identify the source of correlation for each binary response. Regression models of pairwise latent correlation for any two binary response variables are considered to study the association among the multivariate binary response variables.
Using this latent variable approach, one can easily construct the working covariance matrix for parameter estimation using the generalized estimating equation (GEE) approach.
To illustrate the utility of the proposed model, we analyzed a longitudinal data set on metabolic disorders that was collected from a sample of families in Taiwan. Not only the risk assessments of these disorders were conducted but also sources of within-disorder and between-disorder correlations were identified which might be informative to epidemiologists.

1 緒論
1.1 簡介
1.2 邊際效應模型
1.3 隨機效應模型
1.4 研究目標與章節安排
2 Qu的單應變項潛在變數方法
2.1 二元應變項邊際機率模型
2.2 潛在變數
2.3 潛在變數誤差項的隨機效應模型
2.4 廣義估計方程式
2.5 牛頓迭代法11
3 我們所提出的多應變項潛在變數方法
3.1 個別應變項邊際機率模型
3.2 個別應變項潛在變數隨機成份的組成
3.2.1 與王馨儀的方法比較
3.3 雙應變項間相關性的迴歸模型
3.4 參數估計
3.4.1 邊際機率模型參數的廣義估計方程式
3.4.2 變異數成份的廣義估計方程式
3.4.3 雙應變項間相關性模型參數的廣義估計方程式
3.4.4 牛頓迭代法
3.5 參數估計式的穩健變異數
4 實際資料分析
4.1 代謝異常資料的介紹
4.2 個別代謝異常指標資料的分析
4.3 多個代謝異常指標資料的分析
5 總結
5.1 結論與討論
5.2 未來研究
附錄 A
附錄 B
附錄 C
附錄 D
參考文獻

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