Christofides隨機作答設計之邏輯斯迴歸參數估計

Estimation of Parameters of Logistic Regression in Randomized Response Design of Christofides

陳泰宏(Tai-Hong Chen) ； 林家鳴(Jia-Ming Lin) ； 李燊銘(Shen-Ming Lee)

《智慧科技與應用統計學報》 18卷1期 (2020/08) Pp. 1-22

摘要

當在調查較敏感的議題時，會常遇到部分受訪者不誠實作答或拒絕回答，而導致推論上的偏誤，Warner（1965）首先提出隨機作答的設計技巧，以保護受訪者的隱私來爭取受訪者能提供敏感性議題的真實狀況，Christofides（2003）則提供數字化的隨機作答設計，並說明在一些情況下將會優於Warner（1965）的做法。本文將在Christofides（2003）的隨機作答設計下，收集敏感性特徵的訊息，並進一步使用邏輯斯迴歸探討影響敏感性特徵比例的解釋變數議題，除在資料全可觀測到下，提供最大概似估計方法外，也將在有部分解釋變數為隨機缺失下，使用逆選擇機率加權法及無母數多重插補法來提供迴歸參數估計，本文除提供這些估計方法的相關大樣本特性外，也用統計模擬來探討估計方法的表現。

關鍵字

隨機作答設計 ； 敏感性特徵 ； 最大概似估計 ； 逆選擇機率加權法 ； 多重插補法 ； 邏輯斯迴歸

並列摘要

Often, when an interviewer uses a survey to collect the data about sensitive issues, they encounter a serious challenge that the respondents tend to provide untrue answers or refuse to answer. Consequently, the inference based on those data may be incorrect. As the pioneer, Warner (1965) developed the randomized response technique to protect the respondent's privacy, in order to obtain the true answer. Christofides (2003) had developed a version that improved Warner's (1965) randomized response (RR) technique in estimating an unknown proportion of people bearing a sensitive issue in a given community. We use the logistic regression model to estimate the proportion of people bearing sensitive attribute by following the randomized design of Christofides (2003) and provide the maximum likelihood estimators of the regression model. However, it is possible to encounter covariates with missing values in survey studies. Hence, we use the inverse selection probability weighted method and nonparametric multiple imputation method to provide the estimators of regression coefficients when some covariates have missing data. The asymptotic results of the maximum likelihood and inverse selection probability weighted method estimators are established under some regular conditions. We conduct the simulation study to investigate the performance of the proposed estimators and the complete-case analysis.

並列關鍵字

randomized response design ； sensitive characteristic ； maximum likelihood estimator ； inverse selection probability weighted method ； multiple imputation method ； logistics regression