應用一般化Greenberg無關聯隨機作答模式於敏感性問題之研究

A Study on the Sensitive Problems by Using Generalized Greenberg Unrelated Randomized Response Model

10.29973/JCSA.200706.0005

王智立(Chih-Li Wang)；蔡宛容(Wang-Jung Tsai)

敏感性問題 ； 隨機作答模式 ； 比例估計 ； Sensitive question ； randomized response ； estimation of proportion

中國統計學報

45卷2期（2007 / 06 / 01）

189 - 205

繁體中文

在許多問卷訪問過程中，若探討的主題牽涉到敏感性特質時，受訪者往往會基於保護個人隱私或種種心理因素，而產生拒絕回答或不誠實回答的情形，也導致訪員收集的資料不正確而產生估計誤差。為了解決此情形，Warner (1965)首先提出隨機作答模式(Randomized Response Model)，期望藉由隨機作答模式的執行方式，獲得較為可靠的資料以推論敏感性群體比例，除此之外，還可保護受訪者的隱私進而降低受訪者不誠實回答的機率。此後許多學者相繼提出其他的隨機作答程序改良Warner (1965)模式，其最主要的目的皆在於能更準確的估計敏感性問題的效率。其中Greenberg et al. (1969)提出無關聯問題模式(Unrelated-Question Model)，改善Warner (1965)模式中兩個問題皆具敏感性的疑慮，而Christofides (2003)延伸Warner (1965)模式提出了廣義的隨機作答模式，讓受訪者不需要直接回答「是」與「否」，藉以降低不誠實回答的機率。本文考慮將延伸Christofides (2003)所提出的隨機作答模式，並與Warner (1965)模式、Greenberg et al. (1969)的無關聯問題模式作合併，進而提出新的一般化隨機作答模式，文中將可找出敏感性比例的估計量與其變異數。最後，本文將進行一連串的資料模擬，比較在不同參數設計下，本文模式之估計量的效率比較，另外，本文亦說明Warner (1965)與Christofides (2003)模式皆為本文所提模式的特例(special case)。

In the process of many questionnaires, if the topic of study is involves in sensitive characteristics, the participant usually resists or reply untruthfully. It is because of hiding the actual characteristic and protecting the individual privacy or all sorts of psychological factor. The estimated bias is often caused by these dishonest replies or incorrect data. In order to solve the problem, Warner (1965) first proposed ”Randomized Response Model”, and he helps to obtain the reliable data to deduce proportion of the sensitive group by executing this model. Besides, it may raise the protection of participants and reduce the untruthfully reporting probability of the participant. After that, many scholars also proposed other models to improve Warner (1965) model, the main idea is to estimate the efficiency of the sensitive characteristics accurately. Greenberg et al. (1969) proposes Unrelated-Question model, to improve the two questions which both have the sensitive anxiety in Warner (1965) model. Christofides (2003) proposed generalized randomized response model which extended Warner (1965) model, in this model the participant doesn't have to answer 「yes」 and 「no」 directly, and reduces the sensitive level of the participant. This article extends Christofides (2003) model and considers making up Warner (1965) model and Greenberg et al. (1969) Unrelated-Question model, and proposed a generalized randomized response model. In this paper, we can find the estimator and variance of sensitive proportion. The proposed model includes Warner (1965) and Christofides (2003) methods as special cases for a specific choice of the parameters. In addition, a simulating data for the variance of the proposed estimator will be presented.

1. Christofides. T. C.(2003).A generalized randomized response technique.Metrika,57,195-200.
2. Greenberg, B. G.,Abul-Ela, Abdel-Latif, A.,Simmons, W. R.,Horvitz, D. G.(1969).The unrelated question RR model: theoretical framework.J. Amer. Statist. Assoc.,64,520-539.
3. Warner, S. L.(1965).Randomized Response: a survey technique for eliminating evasive answer bias.J. Amer. Statist. Assoc.,60,63-69.

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