在實務應用中，二元反應資料常帶有一些錯誤標記。例如醫學檢驗 的偽陰及偽陽，或是敏感問卷中隨機作答技術導致作答反應值的錯誤分 類。在這些應用中，使用邏輯斯迴歸模型並加入錯誤標記之考量將有助 於建構更準確的統計推論。在本論文我們將研究錯標邏輯斯迴歸模型之 D-最適設計問題。當只有單一解釋變數時，我們發現其D-最適設計與 一般邏輯斯迴歸之D-最適設計同為等權重兩點設計，但這兩個支撐點不 具對稱性。在多個解釋變數的情況下，我們則推廣隨機交換演算法，以 求得錯標邏輯斯迴歸模型的D-最適設計，並討論其與一般邏輯斯迴歸之 結果的異同之處。;In practical applications, binary response data often contain some misclassificationerrors, such as false positives and false negatives in medicaltesting, or response misclassification caused by random response techniquein sensitive questionnaires. Therefore, incorporating misclassification intologistic regression models for such problems can lead to more suitable statisticalinferences. In this thesis, we study D-optimal designs for mislabelledlogistic regression. When there is only one explanatory variable, wefind that there exists a D-optimal design having two support points withequal weights, as that in standard logistic regression, but these two pointsare not symmetric. In the case of multiple explanatory variables, we adaptthe randomized exchange algorithm to obtain a D-optimal design for themislabelled logistic regression and discuss the similarities and differencescompared to the results from the standard logistic regression.
