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題名 混合線性模型推測問題之研究 作者 洪可音 貢獻者 陳麗霞
洪可音關鍵詞 混合線性模型
變異數成份
最佳線性不偏推測量
經驗最佳線性不偏推測量
變異數比率
最大概似法
殘差最大概似法
Mixed linear model
Variance components
Best linear unbiased predictor (BLUP)
Empirical best linear unbiased predictor (EBLUP)
Variance ratio
Maximum likelihood method
Residual maximum likelihood method日期 2000 上傳時間 31-三月-2016 14:44:50 (UTC+8) 摘要 當線性模型中包含隨機效果項時，若將之視為固定效果或直接忽略，往往會造成嚴重的推測偏差，故應以混合線性模型為架構。若模式中只包含一個隨機效果項，則模式中有兩個變異數成份，若包含 個隨機效果項，則模式中有 個變異數成份。本論文主要在介紹至少兩個變異數成份時固定效果及隨機效果線性組合的最佳線性不偏推測量（BLUP），及其推測區間之推導與建立。然而BLUP實為變異數比率的函數，若變異數比率未知，而以最大概似法（Maximum Likelihood Method）或殘差最大概似法（Residual Maximum Likelihood Method）估計出變異數比率，再代入BLUP中，則得到的是經驗最佳線性不偏推測量（EBLUP）。至於推測區間則與EBLUP的均方誤有關，本論文先介紹如何求算其漸近不偏估計量，再介紹EBLUP之推測誤差除以 後，其自由度的估算方法，據以建構推測區間。
When random effects are contained in the model, if they are treated as fixed effects or ignore, then it may result in serious prediction bias. Instead, mixed linear model is to be considered. If there is one source of random effects, then the model has two variance components, while it has variance components, if the model contains random effects. This study primarily presents the derivation of the best linear unbiased predictor (BLUP) of a linear combination of the fixed and random effects, and then the conduction of the prediction interval when the model contains at least two variance components. However, BLUP is a function of variance ratios. If the variance ratios are unknown, we can replace them by their maximum likelihood estimates or residual maximum likelihood estimates, then we can get empirical best linear unbiased predictor (EBLUP). Because prediction interval is relating to the mean squared error (MSE) of EBLUP, so the study first introduces how to get its approximate unbiased estimator, m<sub>a</sub> , then introduces how to evaluate the degrees of freedom of the ratio of the prediction error for the EBLUP and m<sub>a</sub> <sup>1/2</sup> , in order to use both of them to establish the prediction interval.參考文獻 [1] Dempster, A.P. and Selwyn, M.R. (1984), “Statistical and Computational Aspects of Mixed Linear Model Analysis,” Applied Statistics, 33, No.2, 203-214.[2] Harville, D.A. and Carriquiry,A.L. (1992), “Classical and Bayesian Predictions as Applied to an Unbalanced Mixed Linear Model,” Biometrics, 48, 987-1003.[3] Harville, D.A. (1990), BLUP(Best Linear Unbiased Prediction) and beyond, New York: Springer-Veriag.[4] Harville, D.A. and Callanan, T.P. (1990), Computational aspects of likelihood-based inference for variance components, New York: Springer-Veriag.[5] Harville, D.A. and Fenech, A.P. (1985), “Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model,” Biometrics, 41, 137-152.[6] Hulting, F.L. and Harville, D.A.(1991), “Some Bayesian procedures for the analysis of comparative experiments and for small-area estimation: Computational aspects, frequentist properties, and relationships,” Journal of the American Statistical Association, 86, 557-568.[7] Harville, D.A. (1974), “Bayesian inference for variance components using only error contrasts,” Biometrika, 61, 383-385.[8] Jeske. D. R. and Harville, D.A. (1981), “Prediction-interval procedures and (fixed-effects) confidence-interval procedures for mixed linear models, ”Communications in statistics-Theory and Methods, 10, 401-406.[9] Kackar, R.N. and Harville, D.A. (1981), “Unbiasedness of two-stage estimation and prediction procedure for mixed linear models, ” Communications in statistics-Theory and Methods, Sec. A., 10, 1249-1261.[10] Kackar, R.N. and Harville, D.A. (1984), “Approximation for standard errors of estimators of fixed and random effects in mixed linear models, ” Journal of the American Statistical Association, 79, 853-862.[11] McGilchrist, C.A. and Yau, K.K.W (1995), “The Derivation of BLUP, ML, REML Estimation Methods For Generalised Linear Mixed Models,” Commun. Statist.-Theory Meth., 24(12), 2963-2980.[12] Prasad, N.G.N. and Rao, J.N.K.(1990), “The estimation of the mean squared error of small-area estimators,” Journal of the American Statistical Association, 85, 163-171. 描述 碩士
國立政治大學
統計學系
87354018資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001942 資料類型 thesis dc.contributor.advisor 陳麗霞 zh_TW dc.contributor.author (作者) 洪可音 zh_TW dc.creator (作者) 洪可音 zh_TW dc.date (日期) 2000 en_US dc.date.accessioned 31-三月-2016 14:44:50 (UTC+8) - dc.date.available 31-三月-2016 14:44:50 (UTC+8) - dc.date.issued (上傳時間) 31-三月-2016 14:44:50 (UTC+8) - dc.identifier (其他 識別碼) A2002001942 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83248 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 87354018 zh_TW dc.description.abstract (摘要) 當線性模型中包含隨機效果項時，若將之視為固定效果或直接忽略，往往會造成嚴重的推測偏差，故應以混合線性模型為架構。若模式中只包含一個隨機效果項，則模式中有兩個變異數成份，若包含 個隨機效果項，則模式中有 個變異數成份。本論文主要在介紹至少兩個變異數成份時固定效果及隨機效果線性組合的最佳線性不偏推測量（BLUP），及其推測區間之推導與建立。然而BLUP實為變異數比率的函數，若變異數比率未知，而以最大概似法（Maximum Likelihood Method）或殘差最大概似法（Residual Maximum Likelihood Method）估計出變異數比率，再代入BLUP中，則得到的是經驗最佳線性不偏推測量（EBLUP）。至於推測區間則與EBLUP的均方誤有關，本論文先介紹如何求算其漸近不偏估計量，再介紹EBLUP之推測誤差除以 後，其自由度的估算方法，據以建構推測區間。 zh_TW dc.description.abstract (摘要) When random effects are contained in the model, if they are treated as fixed effects or ignore, then it may result in serious prediction bias. Instead, mixed linear model is to be considered. If there is one source of random effects, then the model has two variance components, while it has variance components, if the model contains random effects. This study primarily presents the derivation of the best linear unbiased predictor (BLUP) of a linear combination of the fixed and random effects, and then the conduction of the prediction interval when the model contains at least two variance components. However, BLUP is a function of variance ratios. If the variance ratios are unknown, we can replace them by their maximum likelihood estimates or residual maximum likelihood estimates, then we can get empirical best linear unbiased predictor (EBLUP). Because prediction interval is relating to the mean squared error (MSE) of EBLUP, so the study first introduces how to get its approximate unbiased estimator, m<sub>a</sub> , then introduces how to evaluate the degrees of freedom of the ratio of the prediction error for the EBLUP and m<sub>a</sub> <sup>1/2</sup> , in order to use both of them to establish the prediction interval. en_US dc.description.tableofcontents 封面頁證明書致謝詞論文摘要目錄第一章 緒論1.1 研究動機及目的1.2 論文架構第二章 兩個變異數成份的混合線性模型2.1 模型介紹2.2 估計與推測2.2.1 BLUP與EBLUP2.2.2 變異數比率及變異數之估計2.2.3 的EBULP之運算過程2.3 的BLUP與EBLUP之均方誤差2.3.1 的均方誤差之運算過程2.3.2 推測誤差的抽樣分配2.4 對EBLUP構造的推測區間之修正第三章 多個變異數成份的混合線性模型3.1 模型介紹3.2 估計與推測3.2.1 BLUP與EBLUP3.2.2 變異數比率及變異數之估計3.3 的BLUP與EBLUP之均方誤差3.3.1 的均方誤差之運算過程3.3.2 的均方誤差之運算過程3.4 對EBLUP構造的推測區間之修正第四章 實例分析4.1 實例一4.2 實例二第五章 結論與建議附錄附錄一附錄二附錄三附錄四參考文獻 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001942 en_US dc.subject (關鍵詞) 混合線性模型 zh_TW dc.subject (關鍵詞) 變異數成份 zh_TW dc.subject (關鍵詞) 最佳線性不偏推測量 zh_TW dc.subject (關鍵詞) 經驗最佳線性不偏推測量 zh_TW dc.subject (關鍵詞) 變異數比率 zh_TW dc.subject (關鍵詞) 最大概似法 zh_TW dc.subject (關鍵詞) 殘差最大概似法 zh_TW dc.subject (關鍵詞) Mixed linear model en_US dc.subject (關鍵詞) Variance components en_US dc.subject (關鍵詞) Best linear unbiased predictor (BLUP) en_US dc.subject (關鍵詞) Empirical best linear unbiased predictor (EBLUP) en_US dc.subject (關鍵詞) Variance ratio en_US dc.subject (關鍵詞) Maximum likelihood method en_US dc.subject (關鍵詞) Residual maximum likelihood method en_US dc.title (題名) 混合線性模型推測問題之研究 zh_TW dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Dempster, A.P. and Selwyn, M.R. (1984), “Statistical and Computational Aspects of Mixed Linear Model Analysis,” Applied Statistics, 33, No.2, 203-214.[2] Harville, D.A. and Carriquiry,A.L. (1992), “Classical and Bayesian Predictions as Applied to an Unbalanced Mixed Linear Model,” Biometrics, 48, 987-1003.[3] Harville, D.A. (1990), BLUP(Best Linear Unbiased Prediction) and beyond, New York: Springer-Veriag.[4] Harville, D.A. and Callanan, T.P. (1990), Computational aspects of likelihood-based inference for variance components, New York: Springer-Veriag.[5] Harville, D.A. and Fenech, A.P. (1985), “Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model,” Biometrics, 41, 137-152.[6] Hulting, F.L. and Harville, D.A.(1991), “Some Bayesian procedures for the analysis of comparative experiments and for small-area estimation: Computational aspects, frequentist properties, and relationships,” Journal of the American Statistical Association, 86, 557-568.[7] Harville, D.A. (1974), “Bayesian inference for variance components using only error contrasts,” Biometrika, 61, 383-385.[8] Jeske. D. R. and Harville, D.A. (1981), “Prediction-interval procedures and (fixed-effects) confidence-interval procedures for mixed linear models, ”Communications in statistics-Theory and Methods, 10, 401-406.[9] Kackar, R.N. and Harville, D.A. (1981), “Unbiasedness of two-stage estimation and prediction procedure for mixed linear models, ” Communications in statistics-Theory and Methods, Sec. A., 10, 1249-1261.[10] Kackar, R.N. and Harville, D.A. (1984), “Approximation for standard errors of estimators of fixed and random effects in mixed linear models, ” Journal of the American Statistical Association, 79, 853-862.[11] McGilchrist, C.A. and Yau, K.K.W (1995), “The Derivation of BLUP, ML, REML Estimation Methods For Generalised Linear Mixed Models,” Commun. Statist.-Theory Meth., 24(12), 2963-2980.[12] Prasad, N.G.N. and Rao, J.N.K.(1990), “The estimation of the mean squared error of small-area estimators,” Journal of the American Statistical Association, 85, 163-171. zh_TW
