利用分層隨機抽樣之無關聯問題隨機作答模式研究

A Study on Unrelated-question Randomized Response Model by Using Stratified Random Sampling

王智立(Chih-Li Wang) ； 羅帆志(Fan-Chih Lo)

《智慧科技與應用統計學報》 4卷1期 (2006/06) Pp. 39-62

https://doi.org/10.29807/JTITAS.200606.0003

摘要

從古至今，『敏感性問題』一直是諸多調查者所頭痛的問題，通常與個人隱私相關的問題，都會導致人們不誠實的回答甚至是拒絕作答，因此要獲得真實的訊息較為困難。Warner (1965)首先提出隨機作答模式(Randomized Response model)，希望可以藉由隨機作答模式的執行來收集足夠資料以推論敏感性群體所佔之比例，並且可以增加受訪者的保護感並藉以降低不誠實回答的機率。Greenberg et al. (1969)提出無關聯問題模式(Unrelated-Question model)，改良Warner (1965)模型估計敏感性群體比例之效率，之後有許多學者致力於改良由Warner (1965)模型所發展出來的模型，最重要的目的莫過於更精進於估計敏感性問題的效率，而Hong et al. (1994)提出了等比例抽樣的分層隨機作答模式與Kim & Warde (2004)提出了分層Warner隨機作答模式。
本文考慮將Kim & Warde (2004)提出的分層Warner隨機作答模式與Greenberg et al. (1969)模式做一組合，並假設受訪者會完全誠實作答的情況下，經由證明發現在某些條件限制下，本文所提之模式其估計敏感性群體比例之效率會比上述隨機作答模式來的好。另外，在效率比較方面，吾人將比較在二分層(two strata)條件下本文所提之新方法與Kim & Warde (2004)、Mangat & Singh (1990)、Mangat (1994)及Greenberg et al. (1969)等模式個別比較其估計量之有效性。

關鍵字

敏感性問題 ； 隨機作答模式 ； 分層隨機抽樣

並列摘要

”Sensitive question” has been an issue troubling researcher in the field of statistics. For questions relevant to people's privacy would lead to the consequence that people would answer the questions dishonestly or even refuse to answer, which makes it difficult to obtain the true information. Warner (1965) introduced randomized response model at first to generate enough reliable date to inference the proportion of sensitive group, and to reduce the probability of untrue answer with increases the sense of security of interviewees. Greenberg et al. (1969) introduced unrelated-question model, has improved the efficiency of estimating the proportion of sensitive group of Warner's (1965) model at first, later a lot of scholars were devoted to improving by a great deal of models coming out in development of Warner's (1965) model, the most important purpose of this paper is promoting the validity of estimating the sensitive question, and Hong et al. (1994) introduced a stratified randomized response model and Kim & Warde (2004) introduced a stratified Warner's randomized response model.
The proposed model considers making up Kim & Warde (2004) model and Greenberg et al. (1969) model. Under the assumption of this interviewee are reported truthfully, the proposed model is more efficient than the other models in some specified design of parameters. In addition, we dealt with the empirical study of the relative efficiency of the proposed model with respect to Kim & Warde (2004), Mangat & Singh (1990), Mangat (1994) and Greenberg et al. (1969) in the case of two strata.

並列關鍵字

Sensitive question ； Randomized response model ； Stratified random sampling