當測量誤差(measurement error)和混和效用(mixed effect)同時出現在模型上，文獻上並無太多討論，主因是隨機效用積分後之邊際分配不再是廣義線性模型。本文探討log-linear及logistic模型中有測量誤差及混和效用時之估計方法，在log-linear模型討論常用的測量誤差校正方法包括naive、RC(regression calibration)、SIMEX(simulation extrapolation)、SMEA(small measurement error approximation)外，提出加權校正分數函數，並在重複觀測情況下使用加權、校正再加權之估計方法。而logistic模型除了使用積分取得邊際分配來估計外，利用動差建構估計方程式來估計，在重複觀測下使用部分校正來與未校正作比較。最後用電腦模擬本文所提之估計方法。

When the measurement error and mixed effect appear in the model at the same time, we can not find much discussion on the literature. The main reason is that the marginal distribution of the integral to the random effect is no longer a generalized linear model. This paper discussed the estimated method between measurement error and mixed effect in the log-linear and logistic model. In the log-linear model, the estimation method usually included naive, regression calibration, simulation extrapolation, small measurement error approximation, and there is another estimation method "Weighted and Corrected Score Function" which is weighted, corrected and weighted again under replication situation. The logistic model in addition to use the integral to obtain the marginal distribution, it also used the moment constructed estimated equation to estimate and compared between partial calibration and without calibration under replication situation. At last, it used the computer to simulate the estimated method which was brought up in this paper.

第1章 緒論						1					
第2章 模型問題簡介						4							
§ 2-1 Naive                                             5        
§ 2-2 Regression Calibration；RC                        6        
§ 2-3 Simulation Extrapolation；SIMEX                   6            
§ 2.4 Small Measurement Error Approximation；SMEA       7          
第3章 對數線性模型                                         8         § 3-1 無重複觀測時                                        8      § 3-2 有重複觀測時                                        	9    第4章 邏輯斯模型                                          13       § 4-1 無重複觀測時                                  	13	       § 4-2 有重複觀測時                                	        14      第5章 模擬                                               18          § 5-1 模擬設定                                        	18	   § 5-2 模擬結果                                        	18	   § 5-3 模擬結論                                          	30	   第6章 結論                                                31        附錄	                                                32       
參考文獻                                                  33

C.E. McCulloch, S.R.Searle & J.M.Neuhaus(2008). Generalized, linear, and mixed models. Wiley.
L.A.Stefanski(1985). The effects of measurement error on parameter estimation. Biometrika, 72, 3, pp. 583-592.
N.Wang, X.Lin, R.G.Gutierrez & R.J.Carroll(1998). Bias analysis and SIMEX approach in generalized linear mixed measurement error models. Journal of the American statistical accociation, Vol. 93, No.441.,pp. 249-261. 
R.J.Carroll, D.Rupper, L.A.Stefanski &
C.M.Crainiceanu(2006). Measurement error in nonlinear models. Chapman & Hall, New York.
Zhong, X. P., Fung, W. K. & Wei, B. C. (2002). Estimation in linear models with random effects and errors-in-variables. Ann.Statist. 3, 595-606.
張瑞君(2008). A consistent estimation in log-linear mixed measurement error models. 中華民國淡江大學碩士論文.