敏感问题抽样调查问卷模型的研究及应用
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摘要
沃纳1965年提出随机化回答技术(RRT)后,统计学者在此基础上的研究大致分为两类:一是研究样本获取的抽样方法,希望在不同条件下运用一种抽样方式使得调查最优;二是从改进模型自身入手,以期提高调查效率。本文首先讨论RRT和Warner模型及在此基础上改进的Simmons模型和Greenberg模型;其次介绍敏感性问题调查在简单无放回和分层抽样下的应用,并在此基础上将其推广至各层以简单无放回抽样的分层抽样、群规模大小相等与不相等的整群抽样以及二阶段抽样方式中,同时讨论各自的参数估计,给出了参数表达式。
随着网络信息的高速发展,敏感性问题在网络调查中的应用已成为一个新课题。由于沃纳提出的RRT在实际调查中需要一个随机化装置,费时耗财,无疑增加了调查的难度,同时传统的随机化装置模型在网上调查中也缺乏现实可操作性,因而在社会网络调查中并未得以推广。鉴于此,本文设计出一系列问卷模型,在仍旧保持随机化回答的原则上除去了随机化回答装置,指出此类模型在网上调查中更占有优势,它方便、实用、经济、操作性强,同时我们给出各种问卷模型的具体设计,参数估计表达式及参数的设定。通过理论公式的对比和数值模拟比较各种问卷模型,提出如何选取问卷模型。最后,将问卷模型应用到各类复杂抽样中并给出参数估计表达式。
Since Warner proposed randomized response technique(RRT) in 1965, the research of statistic workers have divided into two categories broadly: one kind is researching the sampling method using a sample of the most excellent under different condition; The others improve the model own in order to improve the survey efficiency. This paper introduces the RRT and the Warner model , Simmons model and Greenberg model first; Followed, introduces the application of the sensitivity sampling survey in simple random sampling without replacement and stratified sampling. We extent it to stratified that each layer using simple random sampling without replacement, and the same-size-group cluster sampling, vary-size-group cluster sampling and two-stage sampling. Also, we discuss their estimation and the parametric expression.
With the rapid development of network, the sensitive question survey online becomes a new topic. Since Warner model needs a randomized device in the actual survey. Because of the device requirement high cost, and unrealistic operation, traditional sensitive question survey based on randomized response technique is hardly to be applied in social survey online. Therefore in view of this we design a series of questionnaire models, still maintaining the principle of randomized response, removing the randomized response device(RRD). We propose that those models are dominate in the online survey ,because they are convenient、practical、economic and feasible. Meanwhile, this paper has given the specific design of variety of questionnaire models, parameter estimation and discussed the parameter setting. Comparison of the theoretical formulas and numerical simulations of various questionnaire models, we give a method of how to select the appropriate model. Finally, take these models into application of various types of complex sample and parameter estimation expressions.
随着网络信息的高速发展,敏感性问题在网络调查中的应用已成为一个新课题。由于沃纳提出的RRT在实际调查中需要一个随机化装置,费时耗财,无疑增加了调查的难度,同时传统的随机化装置模型在网上调查中也缺乏现实可操作性,因而在社会网络调查中并未得以推广。鉴于此,本文设计出一系列问卷模型,在仍旧保持随机化回答的原则上除去了随机化回答装置,指出此类模型在网上调查中更占有优势,它方便、实用、经济、操作性强,同时我们给出各种问卷模型的具体设计,参数估计表达式及参数的设定。通过理论公式的对比和数值模拟比较各种问卷模型,提出如何选取问卷模型。最后,将问卷模型应用到各类复杂抽样中并给出参数估计表达式。
Since Warner proposed randomized response technique(RRT) in 1965, the research of statistic workers have divided into two categories broadly: one kind is researching the sampling method using a sample of the most excellent under different condition; The others improve the model own in order to improve the survey efficiency. This paper introduces the RRT and the Warner model , Simmons model and Greenberg model first; Followed, introduces the application of the sensitivity sampling survey in simple random sampling without replacement and stratified sampling. We extent it to stratified that each layer using simple random sampling without replacement, and the same-size-group cluster sampling, vary-size-group cluster sampling and two-stage sampling. Also, we discuss their estimation and the parametric expression.
With the rapid development of network, the sensitive question survey online becomes a new topic. Since Warner model needs a randomized device in the actual survey. Because of the device requirement high cost, and unrealistic operation, traditional sensitive question survey based on randomized response technique is hardly to be applied in social survey online. Therefore in view of this we design a series of questionnaire models, still maintaining the principle of randomized response, removing the randomized response device(RRD). We propose that those models are dominate in the online survey ,because they are convenient、practical、economic and feasible. Meanwhile, this paper has given the specific design of variety of questionnaire models, parameter estimation and discussed the parameter setting. Comparison of the theoretical formulas and numerical simulations of various questionnaire models, we give a method of how to select the appropriate model. Finally, take these models into application of various types of complex sample and parameter estimation expressions.
引文
[1] Warner S.L.Randomized response: A survey technique for eliminating evasive answer bias[J].J A m Statics Assoc,1965,60(309):63-69
[2] Greenberg, Bernard G., Abul-Ela, Adbed-Latif A., Simmons, Walt R. and Horvitz, Daniel G..The Unrelated Question Randomized Response Model: Theoretical Ramowoek[J], Jour. Amer. Stat. Assoc,1969,64:520-539
[3] Greenberg, Bernard G., Roy R., Kuebler, Jr., Jame R., Abernathy, Daniel G., Horvitz..Application of the Randomized Response Technique in Obtaining Quantitative Data[J] Jour. Amer. Stat. Assoc.1971,66:243-250
[4] Horvitz, D.G., Greenberg, and Abernathy, J.R..:A Data Gathering Device for Sensitive Questions, Internet. Statist. Rew. 44,181-196
[5] Ralph E., Folsom, Bernard G., Greenberg, Daniel G., Horvitz, and James R., Avernathy.The Two Alternate Questions Randomized Response Model for Human Survey, Journal of the American Statistical Association Sep. 1973, Volume 68
[6] N.S. Mangat.An Improved Randomized Response Strategy, J.R. Statist. Soc. B(1994)56,NO. PP. 93-95
[7] Anthony Y.C.Kuk..Asking Sensitive Quesyion Indirectly, Biometrike(1990),77.2.PP. 436-438
[8] J.J.A.Moors.Optimization of the Unrelated Question Randomize Response Model, Journal of the American Statistical Association,1971, 66:627-629
[9]顾震环,解燕,顾莉洁.随机截尾的Warner与Simmons模型,数理统计与管理,2003,5(22):38-42
[10] Pollock K. H.,Bek Y.A.Comparison of Three Randomized Response Models for Quantitative Data[J]. Jour. Amer. Stat. Assoc,1976(1-2):80-86
[11]徐春梅,吕恕.改进的随机截尾模型,统计与信息论坛,2006,21(2):99-102
[12]孙明举,孙山泽,段刚.二项选择敏感性问题调查的基本方法.数理统计与管理, 2000,19(1):58-61
[13]孙明举,孙山泽,段刚.二项选择敏感性问题调查的改进方法.数理统计与管理,2000,7(2):61-63
[14]孙明举,孙山泽,段刚.多项选择随机化调查的多样本模型.数理统计与管理2000,19(3):61-63
[15]孙明举,孙山泽,段刚.多项选择随机化调查的一样本模型.数理统计与管理, 2000,19(2):62-63
[16]吕恕.有多种备选项的敏感问题抽样调查方法分析.电子科技大学学报,1994,3(22):333-336
[17]朱宏,吕恕.敏感性问题抽样调查方法新设计.吉林财贸学院学报,1991,2(2):61-64
[18]李金昌,葛箐.敏感性问题无回答及故意错答的预防与控制.问题研究,2003,5(1):12-15
[19] Chua,T.C, Tsui, A.K.Procuring honest response indirectly, Journal of Statistical Planning and Inference, 2000, 90: 107-116
[20] Winke, R.L. and Framklin,L,A..Warner’s Randomized Response Model: A Bayesian Approach, Jour. Amer. Stat. Assoc., 74(1979)207-214
[21]陈雪如.随机化回答模型中的贝叶斯估计.应用概率统计,1999,3(15):329-331
[22]吕端会,傅珏生.Simmons模型的贝叶斯观点,苏州大学学报,2009,25(1):11-15
[23] kim, J.M., Ward, W.D.(2004).A Stratified Warner’s Randomized Response Model, Journal of Statistical Planning and Inference. 120,155-165
[24] Kim, J.M.(1978).Randomized Response Technique for Temple University, Philadelphia ,USA.
[25]洪志敏,闫在在.分层抽样下的敏感问题研究,内蒙古工业大学学报,2004,23(2)86-89
[26]谢佳斌,王斌会.分层抽样下的西蒙斯随机化回答模型,统计与决策,2007,1:6-8
[27]高歌,范玉波.敏感问题Simmons模型的(分层)整群抽样研究,统计与精算,2009,2:69-75
[28]高歌,范玉波.敏感问题改进的随机应答技术模型分层整群抽样研究及应用,苏州大学学报(医学版)2008;28(5):750-754
[29]闫在在,范金城.辅以分层抽样样本的等容量整群抽样方法,西安交通大学学报,1999,33(12):82-84
[30]卢静莉,闫在在,丁昌江.多元分层抽样样本量的分配,内蒙古工业大学学报,2007,26(2):81-86
[31]朱宏儒,高歌,于明润,王冕,贺志龙,李旭东.数量特征敏感问题分层两阶段整群抽样的统计方法,南京医科大学学报(自然科学版)2009,29(6):909-912
[32] Lanke.On the degree of pretection in randomized interview. International Statistical Review, 1976,44(2): 197-203
[33]闫在在,聂赞坎.随机化策略的公平比较,数学物理学报,2004,24A(3):362-368
[34]张文红,东方社奇.现代抽样新概念-网上抽样调查,统计与决策,1999,9:8-9
[35]范健超.网络环境下敏感性调查的事后分层统计模型,统计与决策,2006,7:29-30
[36]简明.提高网上调查质量的几种方法,统计与决策,2000,7:40
[37]王东.网上调查利弊的方法论权衡和评估,统计与信息论坛,2007,22(4):36-39
[38]黄建.网上调查的误差分析及其控制,统计与决策,2006,6:66-67
[39]孙玉超.对未来网络调查的设想.统计与决策,2007,3:49-50
[40]孙山泽.抽样调查.北京大学出版社,2005,25-26
[41]金勇进,蒋妍,李旭颖.抽样技术.中国人民大学出版社,2002,174-175
[2] Greenberg, Bernard G., Abul-Ela, Adbed-Latif A., Simmons, Walt R. and Horvitz, Daniel G..The Unrelated Question Randomized Response Model: Theoretical Ramowoek[J], Jour. Amer. Stat. Assoc,1969,64:520-539
[3] Greenberg, Bernard G., Roy R., Kuebler, Jr., Jame R., Abernathy, Daniel G., Horvitz..Application of the Randomized Response Technique in Obtaining Quantitative Data[J] Jour. Amer. Stat. Assoc.1971,66:243-250
[4] Horvitz, D.G., Greenberg, and Abernathy, J.R..:A Data Gathering Device for Sensitive Questions, Internet. Statist. Rew. 44,181-196
[5] Ralph E., Folsom, Bernard G., Greenberg, Daniel G., Horvitz, and James R., Avernathy.The Two Alternate Questions Randomized Response Model for Human Survey, Journal of the American Statistical Association Sep. 1973, Volume 68
[6] N.S. Mangat.An Improved Randomized Response Strategy, J.R. Statist. Soc. B(1994)56,NO. PP. 93-95
[7] Anthony Y.C.Kuk..Asking Sensitive Quesyion Indirectly, Biometrike(1990),77.2.PP. 436-438
[8] J.J.A.Moors.Optimization of the Unrelated Question Randomize Response Model, Journal of the American Statistical Association,1971, 66:627-629
[9]顾震环,解燕,顾莉洁.随机截尾的Warner与Simmons模型,数理统计与管理,2003,5(22):38-42
[10] Pollock K. H.,Bek Y.A.Comparison of Three Randomized Response Models for Quantitative Data[J]. Jour. Amer. Stat. Assoc,1976(1-2):80-86
[11]徐春梅,吕恕.改进的随机截尾模型,统计与信息论坛,2006,21(2):99-102
[12]孙明举,孙山泽,段刚.二项选择敏感性问题调查的基本方法.数理统计与管理, 2000,19(1):58-61
[13]孙明举,孙山泽,段刚.二项选择敏感性问题调查的改进方法.数理统计与管理,2000,7(2):61-63
[14]孙明举,孙山泽,段刚.多项选择随机化调查的多样本模型.数理统计与管理2000,19(3):61-63
[15]孙明举,孙山泽,段刚.多项选择随机化调查的一样本模型.数理统计与管理, 2000,19(2):62-63
[16]吕恕.有多种备选项的敏感问题抽样调查方法分析.电子科技大学学报,1994,3(22):333-336
[17]朱宏,吕恕.敏感性问题抽样调查方法新设计.吉林财贸学院学报,1991,2(2):61-64
[18]李金昌,葛箐.敏感性问题无回答及故意错答的预防与控制.问题研究,2003,5(1):12-15
[19] Chua,T.C, Tsui, A.K.Procuring honest response indirectly, Journal of Statistical Planning and Inference, 2000, 90: 107-116
[20] Winke, R.L. and Framklin,L,A..Warner’s Randomized Response Model: A Bayesian Approach, Jour. Amer. Stat. Assoc., 74(1979)207-214
[21]陈雪如.随机化回答模型中的贝叶斯估计.应用概率统计,1999,3(15):329-331
[22]吕端会,傅珏生.Simmons模型的贝叶斯观点,苏州大学学报,2009,25(1):11-15
[23] kim, J.M., Ward, W.D.(2004).A Stratified Warner’s Randomized Response Model, Journal of Statistical Planning and Inference. 120,155-165
[24] Kim, J.M.(1978).Randomized Response Technique for Temple University, Philadelphia ,USA.
[25]洪志敏,闫在在.分层抽样下的敏感问题研究,内蒙古工业大学学报,2004,23(2)86-89
[26]谢佳斌,王斌会.分层抽样下的西蒙斯随机化回答模型,统计与决策,2007,1:6-8
[27]高歌,范玉波.敏感问题Simmons模型的(分层)整群抽样研究,统计与精算,2009,2:69-75
[28]高歌,范玉波.敏感问题改进的随机应答技术模型分层整群抽样研究及应用,苏州大学学报(医学版)2008;28(5):750-754
[29]闫在在,范金城.辅以分层抽样样本的等容量整群抽样方法,西安交通大学学报,1999,33(12):82-84
[30]卢静莉,闫在在,丁昌江.多元分层抽样样本量的分配,内蒙古工业大学学报,2007,26(2):81-86
[31]朱宏儒,高歌,于明润,王冕,贺志龙,李旭东.数量特征敏感问题分层两阶段整群抽样的统计方法,南京医科大学学报(自然科学版)2009,29(6):909-912
[32] Lanke.On the degree of pretection in randomized interview. International Statistical Review, 1976,44(2): 197-203
[33]闫在在,聂赞坎.随机化策略的公平比较,数学物理学报,2004,24A(3):362-368
[34]张文红,东方社奇.现代抽样新概念-网上抽样调查,统计与决策,1999,9:8-9
[35]范健超.网络环境下敏感性调查的事后分层统计模型,统计与决策,2006,7:29-30
[36]简明.提高网上调查质量的几种方法,统计与决策,2000,7:40
[37]王东.网上调查利弊的方法论权衡和评估,统计与信息论坛,2007,22(4):36-39
[38]黄建.网上调查的误差分析及其控制,统计与决策,2006,6:66-67
[39]孙玉超.对未来网络调查的设想.统计与决策,2007,3:49-50
[40]孙山泽.抽样调查.北京大学出版社,2005,25-26
[41]金勇进,蒋妍,李旭颖.抽样技术.中国人民大学出版社,2002,174-175