An extension of the standardized randomized response technique to a multi-stage setup
Tóm tắt
If nonresponse and/or untruthful answering mechanisms occur, analyzing only the available cases may substantially weaken the validity of sample results. The paper starts with a reference to strategies of empirical social researchers related to respondent cooperation in surveys embedding the statistical techniques of randomized response in this framework. Further, multi-stage randomized response techniques are incorporated into the standardized randomized response technique for estimating proportions. In addition to already existing questioning designs of this family of methods, this generalization includes also several (in particular: two-stage) techniques that have not been published before. The statistical properties of this generalized design are discussed for all probability sampling designs. Further, the efficiency of the model is presented as a function of privacy protection. Hence, it can be shown that not one multi-stage design of this family at the same level of privacy protection can theoretically be more efficient than its one-stage basic version.
Tài liệu tham khảo
Barabesi L, Franceschi S, Marcheselli M (2011) A randomized response procedure for multiple-sensitive questions. Statistical Papers (Published online: 27 Feb 2011). doi:10.1007/s00362-011-0374-5
Chang HJ, Wang HL, Huang KC (2004) On estimating the proportion of a qualitative sensitive character using randomized response sampling. Qual Quant 38: 675–680
Chaudhuri A (2001) Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population. J Stat Plan Inference 94: 37–42
Chaudhuri A (2011) Randomized response and indirect questioning techniques in surveys. CRC Press, Boca Raton
Diana G, Perri PF (2009) Estimating a sensitive proportion through randomized response procedures based on auxiliary information. Stat Pap 50: 661–672
Diana G, Perri PF (2011) A class of estimators for quantitative sensitive data. Statistical Papers 52: 633–650
Dillman DA (1978) Mail and telephone surveys: the total design method. Wiley-Interscience, New York
Fidler DS, Kleinknecht RE (1977) Randomized response versus direct questioning: two data-collection methods for sensitive information. Psychol Bull 84: 1045–1049
Giordano S, Perri PF (2011) Efficiency comparison of unrelated question models based on same privacy protection degree. Statistical Papers (Published online: 01 Oct 2011). doi:10.1007/s00362-011-0403-4
Gjestvang CR, Singh S (2007) Forced quantitative randomized response model: a new device. Metrika 66: 243–257
Greenberg BG, Abul-Ela A-LA, Simmons WR, Horvitz DG (1969) The unrelated question randomized response model: theoretical framework. J Am Stat Assoc 64: 520–539
Gross S (1980) Median estimation in sample surveys. In: Proceedings of the survey research methods section of the American statistical association, pp 181–184
Groves RM, Fowler FJ, Couper MP, Lepkowski JM, Singer E, Tourangeau R (2004) Survey methodology. Wiley, Hoboken
Guerriero M, Sandri MF (2007) A note on the comparison of some randomized response procedures. J Stat Plann Inference 137: 2184–2190
Horvitz DG, Shah BV, Simmons WR (1967) The unrelated question randomized response model. In: Social statistics section proceedings of the American statistical association, pp 65–72
Leysieffer FW, Warner SL (1976) Respondent jeopardy and optimal designs in randomized response models. J Am Stat Assoc 71: 649–656
Mahajan PK (2005) Optimum stratification for scrambled response with ratio and regression methods of estimation. Model Assist Stat Appl 1(1): 17–22
Mangat NS (1992) Two stage randomized response sampling procedure using unrelated question. J Indian Soc Agric Stat 44: 82–87
Mangat NS, Singh R (1990) An alternative randomized response procedure. Biometrika 77: 439–442
Mangat NS, Singh S, Singh R (1993) On the use of a modified randomization device in randomized response inquiries. Metron 51: 211–216
Nayak TK (1994) On randomized response surveys for estimating a proportion. Commun Stat Theory Methods 23(11): 3303–3321
Quatember A (2009) A standardization of randomized response strategies. Surv Methodol 35: 143–152
Ryu J-B, Kim J-M, Heo T-Y, Park CG (2005) On stratified randomized response sampling. Model Assis Stat Appl 1(1): 31–36
Särndal C-E, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, New York
Singh R, Singh S, Mangat NS, Tracy DS (1995) An improved two stage randomized response strategy. Stat Pap 36: 265–271
Singh S, Horn S, Singh R, Mangat NS (2003) On the use of modified randomization device for estimating the prevalence of a sensitive attribute. Stat Trans 6: 515–522
Singh S, Sedory SA (2011) Cramer-Rao lower bound of variance in randomized response sampling. Sociol Methods Res 40(3): 536–546
Sitter RR (1992) Comparing three bootstrap methods for survey data. Can J Stat 20(2): 135–154
Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60: 63–69