江金倉臺灣大學：數學研究所黃國華Huang, Guo-HuaGuo-HuaHuang2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/59481本論文針對所觀測群體未知的健康程度或生理機能狀況提出排序方法，其主要考量之資料結構為一群性資料。在此，利用潛藏因子作為個體實際的表徵。對此排序問題，一些適當且廣為使用的潛藏因子及群性量測資料聯合機率模型將作為預測個體潛藏因子數值依據。至於排序方法的評估，我們利用參數化自助重取法產生的潛藏因子數值估計排序指標。此外，更進一步提供簡便及快速計算之估計流程。最後，我們藉助模擬檢視所提出之排序及評估方法，並將此方法應用於一流行病學研究之長期追蹤資料上。Based on cluster measurements, our research interest mainly focuses on seriating the uncertainty in the degree of health or functioning of the body for collected subjects. For this problem, a latent variable is used to represent an unobserved seriation. In this thesis, some adequately and widely used joint models of a latent variable and cluster measurements are proposed to predict the most possible occurring value of a latent variable, which is taken in our seriation procedure. Since a latent variable is considered in modeling, a popular expectation and maximization (EM) algorithm is implemented for the estimation of parameters in the observed likelihood function. Moreover, a parametric bootstrapping method is considered to generate latent values and bootstrap samples, which are used to estimate seriation indices such as the correlation and concordance proportion in the evaluation of seriation. To examine the performance of the developed procedures, a class of simulations is conducted. From the numerical studies, we further detect that the evaluation indices computed based on the maximum likelihood estimators or the true parameters are very close although the accuracy of estimators relies on the sample size. Thus, a computationally efficient approach is proposed to estimate seriation indices. Finally, the seriation and evaluation procedures are applied to a CD4 depletion study.Table of Contents ii List of Tables iii List of Figures v Abstract vi 摘要 vii Acknowledgements viii 1 Introduction 1 2 Joint Model and Estimation 4 2.1 Model..........................................4 2.2 EM-algorithm...................................8 3 Seriation and Evaluation 10 4 Monte Carlo Simulation 12 4.1 Simulation I..................................12 4.2 Simulation II.................................14 5 Application 16 Bibliography 23415578 bytesapplication/pdfen-US群性資料排序潛藏因子自助重取法長期追蹤資料bootstrapping methodcluster dataEM-algorithmlatentthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59481/1/ntu-94-R92221031-1.pdf