本文探討當邏輯斯模型的自變數有測量誤差時，各種不同的估計方法表現的模擬研究。這些方法包含了傳統的迴歸校正、條件分數及新穎的延伸校正分數函數等等。我們考慮有不同的自變數分佈、樣本大小、迴歸參數值、測量誤差變異數與測量誤差分佈等許多情況，並從估計量的樣本變異數或是標準差的大小來評估不同估計方法的效率。

This thesis discusses the performances of different estimation methods in logistic regression model when covariates are subject to measurement errors. The efficiencies of different methods were evaluated through extensively simulation studies. These simulation studies were conducted under different distribution of covariates, samples size, values of regression parameter, the variance associated with measurement errors and the distribution of measurement errors. Conclusions based on the sample standard deviations were derived.

第一章 緒論				          1
第二章 邏輯斯模型之傳統估計方法		          4
第2.1節 符號定義                                          4
第2.2節 各種邏輯斯模型之估計方法介紹                      4
第三章 延伸校正分數函數與誤差增量                         9
第3.1節 延伸校正分數                                      9
第3.2節 誤差增量                                         10
第四章 模擬                                              12
第4.1節 模擬條件與符號定義                               12
第4.2節 模擬結果                                         13
第五章 結論                                              15
參考文獻                                                 16

Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Errors in Nonlinear Models: A Modern Perspective. Second Edition. Chapman & Hall, London.

Huang, Y. and Wang, C. Y. (2001). Consistent Functional Methods for Logistic Regression with Errors in Covariates. Journal of the American Statistical Association 96, 1469-1482.

Nakamura, T. (1990). Corrected score functions for errors-in-variables models: Methodology and application to generalized linear models. Biometrika 77, 127-137.

Stefanski, L. A. and Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement error models. Biometrika 74, 703-716.

楊喬閔(2012). Extended corrected-score in generalized linear models. 中華民國淡江大學碩士論文.