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系統識別號 U0002-2107201410411800
中文論文名稱 具有隨機效應及測量誤差之對數線性模型的參數估計方法
英文論文名稱 The Estimation of the Log-Linear Model with Measurement Errors and Random Effects
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 102
學期 2
出版年 103
研究生中文姓名 丁怡皓
研究生英文姓名 Yi-Hao Ting
學號 601190282
學位類別 碩士
語文別 中文
口試日期 2014-06-24
論文頁數 31頁
口試委員 指導教授-黃逸輝
委員-温啟仲
委員-黃文瀚
中文關鍵字 測量誤差  隨機效應  對數線性模型  延伸校正QVF估計法 
英文關鍵字 Measurement error  Random effect  Log-linear model  Extended corrected QVF score 
學科別分類 學科別自然科學數學
中文摘要 在自變數有測量誤差時,具有隨機效用的廣義線性模式的分析相當困難,主要原因是將隨機效用積分後的分配已不再是廣義線性模式,使得傳統上處理測量誤差的條件分數法或是校正分數法難以應用。本文主要探討對數線性在有測量誤差和隨機效用時的模型中,提出使用延伸校正QVF(quasilikelihood and variance function)的估計法,並與 Naive 、迴歸校正法及部分條件分數法三者作模擬比較。
英文摘要 There are not many literatures discuss the statistical inference when
the measurement error and random effect exist in the generalized linear
model. The main reason is that the distribution after integrating the random
effect is no longer a generalized linear model, hence the conventional
conditional score or corrected score are difficult in application. This
paper discussed the estimation method when measurement error and random
effect coexist in the log-linear model, the estimation was done by an
extended corrected QVF score. We compare the efficient of the methods of
Naive, regression calibration and partially conditional score with the
proposed method by simulation studies.
論文目次 目錄
第1章緒論 1
第2章自變數含有測量誤差之對數線性隨機效應模型 4
2.1 符號的定義 4
2.2 模型 5
第3章估計方法 7
3.1 Naive 估計法 7
3.2 迴歸校正法(Regression Calibration ; RC) 8
3.3 部分條件分數法(Partially Conditional Score) 9
3.4 延伸校正QVF估計法(QVF-EXCR) 10
第4章模擬研究 15
4.1 模擬設定 15
4.2 模擬結果 16
第5章結論 18
參考文獻 30
參考文獻 參考文獻
Carroll, R. J., Rupper, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Mea-
surement error in nonlinear models. Chapman and Hall, New York.
Chan, Jennifer S.K. and Kuk, Anthony Y.C. (1997). Maximum Likelihood Estimation
for Probit-Linear Mixed Models with Correlated Random Effects. Biomet-
rics, 53, No. 1, 86-97.
Hengjian, C., Kai, W. N. and Lixing, Z. (2004). Estimation in mixed effects model
with error in variables. Journal of Multivariate Analysis 91, 53-73.
Nakamura, T. (1990). Corrected Score Function for Errors-in-Variables Models:
Methodology and Application to Generalized Linear Models. Biometrika, 77,
No. 1, 127-137.
Novick, S. J. and Stefanski, L. A. (2002). Corrected score estimation via complex
variable simulation extrapolation. Journal of the American Statistical Associa-
tion 97, 472-481.
Schall, R. (1991). Estimation in Generalized Linear Models with Random Effects.
Biometrika, 78, No. 4, 719-727.
Stefanski, L. A. and Carroll, R. J. (1987). Conditional Scores and Optimal Scores
for Generalized Linear Measurement- Error Models. Biometrika, 74, No. 4,
703-716.
Wang, N., Lin, X., Gutierrez, R. G., Carroll, R. J. (1998). Bias Analysis and SIMEX
Approach in Generalized Linear Mixed Measurement Error Models. Journal of
the American Statistical Association, 93, No. 441, 249-261.
Zhong, X., Fung, W., and Wei, B. (2002). Estimation in linear models with random
effects and errors-in-variables. Ann. Inst. Statist. Math. 54, No. 3, 595-606.
余佳倫(2012). On the estimation methods for the generalized linear mixed effect
model with measurement error. 中華民國淡江大學碩士論文.
林承翰(2013). The estimation of the logistic regression model with measurement
errors and random effects. 中華民國淡江大學碩士論文.
張瑞君(2009). A consistent estimation in log-linear mixed measurement error models.
中華民國淡江大學碩士論文.
楊喬閔(2012). Extended corrected-score in generalized linear models. 中華民國淡江大學碩士論文.
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