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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 蕭朱杏 | |
dc.contributor.author | Miao-Yu Tsai | en |
dc.contributor.author | 蔡秒玉 | zh_TW |
dc.date.accessioned | 2021-06-13T16:55:50Z | - |
dc.date.available | 2006-06-13 | |
dc.date.copyright | 2005-06-13 | |
dc.date.issued | 2005 | |
dc.date.submitted | 2005-06-07 | |
dc.identifier.citation | Aerts, M., Geys, H., Molenberghs, G. and Ryan, L. M (2002), Topics in Modeling of Clustered Data, London: Chapman & Hall.
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(1982), “Random-effects models for longitudinal data,” Biometrics, 38, 963-974. Liang, K. Y., and Zeger, S. L. (1986), “Longitudinal data analysis using generalized linear models,” Biometrics, 73,13-22. Liang, K. Y. and Zeger, S. L. (1989), “A class of logistic regression models for multivariate binary time series,” Journal of the American Statistical Association, 84, 447-451. Liang, K. Y., Zeger, S. L. and Qaqish, B. (1992), “Multivariate regression analysis for categorical data,” Journal of the Royal Statistical Society, Ser. B, 54, 3-40. Margaret, A. C. and Liang, K. Y. (1988), “Conditional logistic regression models for correlated binary data,” Biometrika, 75, 501-506. Natarajan, R. and Kass, R. (2000), “Reference Bayesian methods for generalized linear mixed models,” Journal of the American Statistical Association, 95, 227-237. Pauler, D. K. (1998), “The Schwarz criterion and related methods for normal linear models,” Biometrika, 85, 13-27. Pauler, D. K., Wakefield, J. C. and Kass, R. E. (1999), “Bayes factors and approximations for variance component models,” Journal of the American Statistical Association, 94, 1242-1253. Prentice, R. L. (1986), “Binary regression using an extended Beta-Binomial distribution, with discussion of correlation induced by covariate measurement errors,” Journal of the American Statistical Association, 81, 321-327. Rao, C. R. and Rao, M. B. (1998), Matrix Algebra and its Applications to Statistics and Econometrics, Singapore: World Scientific. Robert, C. P. (2001), The Bayesian Choice: A Decision Theoretic Motivation, 2nd Edition, New York: Springer-Verlag. Rosner, B. (1984), “Multivariate methods in ophthalmology with application to other paired-data situations,” Biometrics, 40, 1025-1035. Rosner, B. (1989), “Multivariate methods for clustered binary data with more than one level of nesting,” Journal of the American Statistical Association, 84, 373-380. Rosner, B. 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(1991), “Generalized linear models with random effects; a gibbs sampling approach,” Journal of the American Statistical Association, 86, 79-86. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38985 | - |
dc.description.abstract | 在生物醫學統計中常接觸到具有相關性的資料,這些相關性可能是基因、環境、重複測量或是時間所造成的;在這一類型的研究中,我們通常不只對治療的效用有興趣,觀測值的變異以及觀測值之間的相關性亦可能是我們所關注的量,這些變異或相關形式都可以被稱為變異數成份(variance components)。
傳統的統計方法會使用有限制最大概似(restricted maximum likelihood, REML)估計法來估計變異數成份;貝氏統計分析則利用後驗分配來作推論。在廣義線性混合模式下,我們證明了在樣本數很大時,隨機效應之變異數成份的後驗眾數和REML估計值會近似相等(asymptotically equivalent),同時也建立了後驗眾數和REML估計值的近似關係式,並提出了比較二種後驗眾數與REML估計值之間遠近的準則。我們利用此準則證明了以approximate Jeffreys’ prior為變異數成份的先驗分配,會比以approximate uniform shrinkage為變異數成份的先驗分配所得到的後驗眾數較接近REML估計值;而在有限樣本的模擬結果也有同樣的結果。最後,本文提出了連續型和離散型的兩個實例分析。 | zh_TW |
dc.description.abstract | Longitudinal and correlated data are commonly modeled with generalized linear mixed models (GLMM) which contain both fixed and random effects. The source of the random effect may come from the genetic heredity, familial aggregation, or environmental heterogeneity. The inference of its variance component is usually difficult due to the dimension of its covariance matrix (more than one random effect) and the complexity of the likelihood function. In this research, we discuss the restricted maximum likelihood (REML) estimation of variance components, and focus mainly on the Bayesian approach with posterior distribution. We will demonstrate the specification of reference prior distribution on the random covariance matrix. We will consider the approximate uniform shrinkage prior and approximate Jeffreys’ prior. Both are formulated based on the approximated likelihood function. Under generalized linear mixed models, we show that the posterior mode under Jeffrey’s prior is asymptotically closer to the REML estimate than the mode under uniform shrinkage prior does. In fact, the relative distance converges to a positive integer for any square random matrix. We also conduct the formal Bayesian inference of the variance components using posterior samples obtained by Markov chain Monte Carlo method. Finally, we consider two real applications and simulation studies for the purpose of illustration. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T16:55:50Z (GMT). No. of bitstreams: 1 ntu-94-D90842004-1.pdf: 2022468 bytes, checksum: e787a9901825fe160dbb1e8fbeb29ee2 (MD5) Previous issue date: 2005 | en |
dc.description.tableofcontents | 第一章 研究背景與動機 1
第一節 現有估計變異數的方法 2 第二節 變異數成份的事前分配 4 第三節 研究動機 5 第二章 變異數成份在不同模式下之推論與先驗分配設定的文獻探討 8 第一節 固定效應模式(Fixed effects models)下之估計 8 一、 變異數分析(ANOVA) 9 二、 線性模式(Linear models)與有限制概似函數 9 第二節 隨機截距項模式(Random intercept models)下之估計 13 第三節 混合效應模式(Mixed effects models)下之估計 17 一、 線性混合效應模式(Linear mixed effects models) 17 二、 廣義線性混合效應模式(Generalized linear mixed models) 25 第三章 比較變異數成份之後驗分配眾數的點估計 32 第一節 變異數成份為一維的情況 33 一、 REML估計值 34 二、 後驗眾數估計值 36 第二節 變異數成份為二維的情況 41 一、 後驗分配的近似 41 二、 比較approximate uniform shrinkage和approximate Jeffreys’ prior 46 第三節 變異數成份為多維的情況 52 一、 後驗分配的近似 52 二、 以Breslow & Clayton (1993)的近似方法求得approximate Jeffreys’ prior 54 三、 比較approximate uniform shrinkage和兩種approximate Jeffreys’ prior 55 第四章 模擬 59 第一節 Markov chain Monte Carlo (MCMC)方法 59 一、 固定效應 的條件分配 與其抽樣 59 二、 隨機效應 的條件分配 與其抽樣 61 三、 變異數矩陣 的條件分配 與其抽樣 62 第二節 當 是連續型資料的情況 64 第三節 當 是離散型資料的情況 74 第四節 結論與建議 79 第五章 實例分析 81 第一節 兒童近視防治臨床試驗(Myopia Intervention Trial) 81 第二節 癲癇症發作次數臨床試驗(Epileptic Seizure Study) 90 第六章 討論與建議 93 第一節 總結 93 第二節 討論與建議 95 一、 使用Markov chain Monte Carlo方法的問題 96 二、 不可積分的先驗分配(Improper prior) 97 三、 後驗眾數和後驗平均數的選擇 99 第三節 未來研究方向 101 參考文獻………………………………………………………………102 附錄一 後驗分配的近似 108 附錄二 對approximate uniform shrinkage和Natarajan & Kass (2000)所得到的approximate Jeffreys’ prior取logarithm後的一階微分的推導 110 附錄三 一維的變異數成份之模擬結果 113 附錄四 變異數成份 、 和 的REML估計值及後驗眾數和平均數估計值的估計結果(包含非對角線參數估計結果) 125 附錄五 以連續型資料為例,假設多維變異數成份為獨立,並以inverted gamma作為個別的假設分配之模擬分析 129 模擬程式………………………………………………………………134 表 目 錄 表4-1:連續型資料模擬的固定效應之MLE和三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 65 表4-2:連續型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 72 表4-3:連續型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 72 表4-4:連續型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 73 表4-5:比較連續型資料模擬的REML和三種後驗估計值之平方誤差危險 73 表4-6:比較連續型資料模擬的REML和三種後驗估計值與真值之平方距離 73 表4-7:比較連續型資料模擬的REML與三種後驗估計值之平方距離 74 表4-8:離散型資料模擬的固定效應 之MLE和三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 75 表4-9:離散型資料模擬的固定效應 之MLE和三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 76 表4-10:離散型資料模擬的固定效應 之MLE和三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 76 表4-11:離散型資料模擬的固定效應 之MLE和三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 77 表4-12:離散型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 77 表4-13:離散型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤、均方誤差和均方相對誤差 78 表4-14:離散型資料模擬的變異數成份 之REML估計值及三種後驗估計值的平均數、標準誤和均方誤差 78 表4-15:比較離散型資料模擬的三種後驗估計值與真值之平方距離 78 表5-1:MIT資料的固定效應之MLE及後驗眾數和平均數估計值 88 表5-2:MIT資料的變異數成份之REML及後驗眾數和平均數估計值;小括號內數值為95%可信區間(credible interval) 89 表5-3:ESS資料的固定效應之MLE及後驗眾數和平均數估計值 91 表5-4:ESS資料的變異數成份之REML及後驗眾數和平均數估計值;小括號內數值為95%可信區間(credible interval) 92 圖 目 錄 圖4-1:以Breslow & Clayton (1993)的approximate Jeffreys’ prior作為變異數成份的先驗分配所得到5000個後驗樣本的散佈圖 66 圖4-2:以Natarajan & Kass (2000)的approximate Jeffreys’ prior作為變異數成份的先驗分配所得到5000個後驗樣本的散佈圖 67 圖4-3:以approximate uniform shrinkage作為變異數成份的先驗分配所得到5000個後驗樣本的散佈圖 68 圖5-1:MIT資料之188位兒童的右眼近視度數時間趨線圖 84 圖5-2:MIT資料之188位兒童的左眼近視度數時間趨線圖 85 圖5-3:MIT資料之188位兒童左右眼前房深度的時間趨線圖 85 圖5-4:MIT資料之188兒童左右眼的近視度數和前房深度相關性的時間趨勢圖……………………………………………………86 | |
dc.language.iso | zh-TW | |
dc.title | 變異數成份在廣義線性混合模式下之貝氏統計推論 | zh_TW |
dc.title | Bayesian Inference of Variance Components in Generalized Linear Mixed Models | en |
dc.type | Thesis | |
dc.date.schoolyear | 93-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 陳宏,樊采虹,陳素雲,張淑惠,戴政 | |
dc.subject.keyword | GLMM,REML,variance component,MCMC,uniform shrinkage prior,Jeffreys’ prior, | zh_TW |
dc.subject.keyword | Jeffreys’ prior,MCMC,uniform shrinkage prior,REML,variance component,GLMM, | en |
dc.relation.page | 150 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2005-06-07 | |
dc.contributor.author-college | 公共衛生學院 | zh_TW |
dc.contributor.author-dept | 流行病學研究所 | zh_TW |
顯示於系所單位: | 流行病學與預防醫學研究所 |
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