臺灣博碩士論文加值系統

一般說來，在調查訪問過程中，若是訪員詢問的主題為敏感性問題時，受訪者通常會基於保護個人隱私或種種心理因素，而採取拒絕回答或不誠實回答來隱藏實際情形，這些不誠實的回答所造成的誤差，使得敏感性問題的統計資料往往較不準確。為改善此種現象，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獲得可靠的資料以推論敏感性群體比例，並可提高受訪者隱私的保護進而降低受訪者不誠實回答的機率。之後釵h學者也提出了其他的隨機作答程序來改良Warner(1965)模式，其最主要的目的在於能更準確的估計敏感性問題的效率。其中以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)程序提出了廣義的隨機作答程序，讓受訪者不需要直接回答「是」與「否」，藉以降低受訪者之敏感性。
本文考慮將Christofides(2003)提出的隨機作答模式做一延伸，與Greenberg et al.(1969)的無關聯問題模式（Unrelated-Question model）作結合，而提出二種新的隨機作答模式，文中可找到敏感性比例的估計量與其變異數。此外，本文將加入分層抽樣的概念並進行一連串的資料模擬，藉此與其他隨機作答模式做效率（efficiency）比較。

Generally speaking, in the process of investigation, when the inquiry subjects are sensitive question, the participant usually resists or reply untruthful to hide the actual characteristic to protect the individual privacy or all sorts of psychological factor. The bias of these dishonest replies causes the statistical data often plate out of true. Warner (1965) first proposed “Randomized Response model”, and he helps to obtain the reliable to deduce proportion of the sensitive group by executing this model. It may raise the protection of participants and reduce the probability which the participant untruthful replied. After that, many scholars also proposed other models to improve Warner (1965) model. Greenberg et al. (1969) proposes Unrelated-Question model, to improve the two questions which have the sensitive anxiety in Warner (1965) model. Christofides (2003) proposed generalized randomized response which extended Warner (1965) model. The participant does not have to answer 「yes」 and 「no」 directly, and reduces the sensitive of the participant.
This article extends Christofides (2003) model and considers making up Christofides (2003) model and Greenberg et al. (1969) Unrelated-Question model, and proposed two kinds of alternative randomized response models. In this paper, we can find the estimator and variance of sensitive proportion. The model includes Warner’s (1965) and Christofides (2003) methods as special cases for a specific choice of the parameters. In addition, a simulating data with stratified sampling for the variance of the proposed estimator will be presented.

中文摘要....................................................................................................I
英文摘要...................................................................................................II
誌謝..........................................................................................................III
目錄..........................................................................................................IV
圖目錄......................................................................................................VI
表目錄....................................................................................................VII
第一章 緒論...........................................................................................1
第一節 研究動機與目的...................................................................1
第二節 研究流程...............................................................................2
第三節 研究架構...............................................................................3
第二章 文獻探討...................................................................................5
第一節 Warner隨機作答模式...........................................................5
第二節 無關聯問題隨機作答模式...................................................7
一、 已知比例之無關聯問題隨機作答模式...............................7
二、 未知比例之無關聯問題隨機作答模式...............................8
第三節 Christofides隨機作答模式.................................................10
第四節 分層隨機作答模式.............................................................12
第五節 Christofides分層隨機作答模式.........................................14ㄧ、 每一層中的隨機裝置皆相同.............................................14
二、 每一層中的隨機裝置不相同.............................................15
第三章 廣義隨機作答模式之研究方法.............................................16
第一節 廣義隨機作答模式.............................................................16
第二節 分層廣義隨機作答模式.....................................................22
第三節 數值模擬............................................................................ 30
第四節 效率比較.............................................................................35
第四章 一般隨機作答模式之研究方法............................................ 44
第一節 一般隨機作答模式............................................................ 44
第二節 分層一般隨機作答模式.................................................... 49
第三節 數值模擬............................................................................ 55
第四節 效率比較.............................................................................60
第五章 模式比較................................................................................ 69
第一節 廣義隨機作答模式與一般隨機作答模式之效率比較.... 69
第二節 分層廣義隨機作答模式與分層一般隨機作答模式之效率比較.................................................................................... 73
第六章 結論與建議.............................................................................79
參考文獻..................................................................................................82

參考文獻

[1] Chaudhuri, A. and Mukerjee, R., Randomized Response- Theory and Techniques, 1988, pp. 1-81.
[2] Christofides. T. C.（2003）, A generalized randomized response technique, Metrika, Vol. 57, pp. 195-200.
[3] Christofides. T. C.（2005）, “Randomized response in stratified sampling”, Journal of Statistical Planning and Inference, Vol. 128, pp. 303-310.
[4] Greenberg, B. G., Abul-Ela, Abdel-Latif, A., Simmons, W. R., and Horvitz, D. G.（1969）, “The unrelated question RR model：theoretical framework”, Journal of American Statistical Association, Vol. 64, pp. 520-539.
[5] Hong, K., Yum, J., Lee, H., (1994) “A Stratified Randomized Response Technique”, Korean J. Appl. Statist. Vol.7, pp. 141-147.
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[7] Kim, J. M. and Warde, W. D.（2004）, “A stratified Warner''s randomized response model”, Journal of Statistical Planning and Inference, Vol. 120, pp. 155-165.
[8] Warner, S. L.（1965）, “Randomized Response：a survey technique for eliminating evasive answer bias”, Journal of American Statistical Association, Vol. 60, pp. 63-69.