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分層隨機作答模式於敏感性問題之一般化研究

A Generalized Study of Sensitive Problems by Using Stratified Randomized Response Model

摘要


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,所以,較具敏感性問題的統計資料通常是缺乏或不精確的。爲解決此一情形,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方式來獲得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。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)模式提出新的隨機作答模式,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。本論文的重點在於如何應用隨機實驗來協助隨機作答程序的進行,以期在實務運用上,可以降低訪問的敏感程度,減低受訪者的排拒心及保障受訪者的隱私,以獲得更好的比例估計值或訪問品質。具體的成果有:(1).將分層隨機抽樣設計應用到Christofides(2003)之隨機作答模式上,並與Warner (1965)、Greenberg et al.(1969)的無關聯問題模式作一合併,進而提出兩種新的隨機作答模式,文中將可找出敏感性比例的估計量與其變異數。(2)藉由資料模擬之方式比較在不同參數設計下,本文模式與Warner(1965)、Christofides(2003)模式之估計量的效率比較。(3)文中亦說明在相同的參數設計下,Warner(1965)與Christofides(2003)模式皆爲本文所提模式的特例(special cases)。

並列摘要


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. Hence, static data or estimates concerning sensitive question are usually very insubstantial and inaccurate. In order to solve this 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 probability which the participant untruthful replied. 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 a new randomized response which extended Warner (1965) model. The participant doesn't have to answer 「yes」 and 「no」 directly, and reduces the sensitive level of the participant. This article mainly focuses on how to employ random trials to assist the progress of randomized response procedure so that the rejection rate of interview can be reduced and the privacy of interviewees is well protected. Better ratio estimate and interview qualities are expected to obtain. Toward this purpose, the following works have been done: (1) We apply the stratified random sampling design to generalized Christofides (2003) randomized response model. Two new generalized models for the sensitive problems, which is an integration of Warner (1965), Greenberg et al. (1969) and Christofides (2003) model, is proposed. In this paper, we also can find the estimator and variance of sensitive proportion. (2) We want to compare the performance of estimation with Warner (1965) and Christofides (2003) model, by data simulating. (3) The proposed models include Warner (1965) and Christofides (2003) methods as special cases for a specific choice of the parameters.

參考文獻


王智立、蔡宛容(2007)。應用一般化Greenberg無關聯隨機作答模式於敏感性問題之研究。中國統計學報。45(2),190-207。
Christofides, T. C.(2003).A Generalized Randomized Response Technique.Metrika.57(2),195-200.
Christofides, T. C.(2005).Randomized Response in Stratified Sampling.Journal of Statistical Planning and Inference.128(1),303-310.
Greenberg, B. G.,Abul-Ela, A. A.,Simmons, W. R.,Horvitz, D. G.(1969).The Unrelated Question Randomized Response Model: Theoretical Framework.Journal of the American Statistical Association.64(326),520-530.
Kim, J. M.,Warde, W. D.(2004).A Stratified Warner's Randomized Response Model.Journal of Statistical Planning and Inference.120(1-2),155-165.

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