在隨機作答技巧下敏感性特徵比例之貝氏推論

Bayes Estimation of Proportions to Sensitive Attribute of Randomized Response Technique

劉怡均(Yi-Chun Liu) ； 李燊銘 (Shen-Ming Lee) ； 彭德昭(Ter-Chao Peng) ； 高秀蘭 (Shiow-Lan Gau)

《智慧科技與應用統計學報》 14卷1期 (2016/06) Pp. 15-34

摘要

對於涉及個人隱私之敏感性特徵的訊息常使用問卷調查的方式收集，但受訪者面對陌生的訪員來進行面訪時，要直接回答或填答涉及個人隱私之敏感性問題將會有嚴重的壓力，受訪民眾將可能會不回答或提供不實的答案，而使用隨機作答的調查方式則有助於隱私的保護，以爭取受訪者的誠實回答。Greenberg et al. (1969)提出不相關問題的隨機作答設計，並提供敏感性特徵的比例估計，但在實務上有時會遭遇此估計不是在(0,1)區間內，故本文在此隨機作答設計下，將引入潛在變數概念及使用貝氏方法結合吉氏抽樣法(Gibbs sampling)來提供敏感性特徵比例的估計。本文也將用統計模擬來評估Greenberg et al.(1969)與提出貝氏估計方法的表現，同時也使用隨機作答設計方法於2012 年「台灣社會變遷基本調查」中收集外遇的訊息及2004 年台灣地區有線電視收視戶調查中收集私接收看之訊息，以評估台灣地區外遇比例及有線電視私接率。

關鍵字

隨機作答設計 ； 貝氏方法 ； 吉氏抽樣 ； 台灣社會變遷基本調查 ； 外遇比例 ； 有線電視私接率

並列摘要

Personal information regarding the sensitive traits or attributes are usually obtained by conducting a questionnaire survey. In order to provide an answer to the questions on sensitive matters to the interviewer, the interviewee undergoes some stress. Often, the interviewee (respondent) would not be willing to provide accurate or true responses. The randomized response technique offers some guarantees for protecting the respondent's privacy without revealing his or her respondent identity. The use of some randomized devices brings the respondent to the point of providing truthful answers to the sensitive questions. Greenberg et al. (1969) proposed the unrelated randomized response technique and the estimation of the proportion of the sensitivity attribute. However, in some practical examples (cases), this estimate may not lie within the (0, 1) interval. In this study, we introduce the concept of latent variable and use of the Bayesian method combined with the Gibbs sampling methods to provide the estimators of the proportion of the sensitivity attribute based on the unrelated randomized response technique proposed by Greenberg et al. (1969). We conduct a simulation study to investigate the performance of the proposed Bayesian method and the Greenberg et al.'s (1969) method. In addition, we use two real examples including, the extramarital relationship, a case study of Taiwan Social Change Survey in 2012, and an unauthorized cable TV, a data study of Taiwan Cable TV Viewing Households Survey in 2004 to infer the proportions of extramarital relationship and of unauthorized cable TV users in Taiwan, respectively.

並列關鍵字

Randomized response technique ； Bayesian method ； Gibbs sampling ； Taiwan Social Change Survey (TSCS) ； Proportion of extramarital relationships ； Proportion of unauthorized cable TV users