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| Title: | 混合線性模型推測問題之研究 |
| Authors: | 洪可音 |
| Contributors: | 陳麗霞
洪可音 |
| Keywords: | 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 |
| Date: | 2000 |
| Issue Date: | 2016-03-31 14:44:50 (UTC+8) |
| Abstract: | 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. |
| Reference: | [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. |
| Description: | 碩士
國立政治大學
統計學系
87354018 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#A2002001942 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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