Abstract
A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two-stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non-sensitive group. The randomization is implemented on the basis of Franklin’s procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum-likelihood or moment estimation.
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Barabesi L (1998) The computation of the distribution of the sign test statistic for ranked-set sampling. Commun Stat Simulation Comput 27: 833–842
Barabesi L (2008) A design-based randomized response procedure for the estimation of population proportion and sensitivity level. J Stat Plan Inf 138: 2398–2408
Barabesi L, Greco L (2002) The exact computation of the Student t, Snedecor F and sample correlation coefficient distribution functions. J Royal Stat Soc D 51: 105–110
Barabesi L, Marcheselli M (2006) A practical implementation and Bayesian estimation in Franklin’s randomized response procedure. Commun Stat Simulation Comput 35: 563–573
Bar-Lev SK, Bobovich E, Boukai B (2003) A common conjugate prior structure for several randomized response models. Test 12: 101–113
Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, New York
Chang HJ, Huang KC (2001) Estimation of proportion and sensitivity of a qualitative character. Metrika 53: 269–280
Chaudhuri A, Mukerjee R (1985) Optionally randomized response technique. Calcutta Stat Assoc Bull 34: 225–229
Chaudhuri A, Mukerjee R (1988) Randomized response: theory and techniques. Dekker, New York
Chaudhuri A, Saha A (2005) Optimal versus compulsory randomized response techniques in complex surveys. J Stat Plan Inf 135: 516–527
Franklin LA (1989) A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Commun Stat Theory Methods 18: 489–505
Gjestvang CR, Singh S (2006) A new randomized response model. J Royal Stat Soc B 68: 523–530
Horvitz DG, Shah BV, Simmons WR (1967) The unrelated question randomized response model. Proceedings of the ASA Social Statistics Section, pp 65–72
Huang KC (2004) A survey technique for estimating the proportion and sensitivity in a dichotomous finite population. Stat Neerlandica 58: 75–82
Kim JM, Tebbs JM, An SW (2006) Extension of Mangat’s randomized response model. J Stat Plan Inf 136: 1554–1567
Kuk AYC (1990) Asking sensitive questions indirectly. Biometrika 77: 436–438
Lensvelt-Mulders GJLM, Hox JJ, van der Heijden PGM, Maas CJM (2005) Meta analysis of randomized response research: thirty-five years of validation studies. Sociological Methods Res 33: 319–348
Liu PT, Chow LP (1976) The efficiency of multiple trial randomized response technique. Biometrics 32: 607–618
Mangat NS (1994) An improved randomized response strategy. J Royal Stat Soc B 56: 93–95
Mangat NS, Singh R (1990) An alternative randomized response procedure. Biometrika 77: 439–442
Marcheselli M, Barabesi L (2006) A generalization of Huang’s randomized response procedure for the estimation of population proportion and sensitivity level. Metron LXIV: 145–159
Migon HS, Tachibana VM (1997) Bayesian approximations in randomized response model. Comput Stat Data Analy 24: 401–409
Singh R, Mangat NS (1996) Elements of survey sampling. Kluwer, Dordrecht
Singh S (2003) Advanced sampling theory with applications. Kluwer, Dordrecht
Unnikrishnan NK, Kunte S (1999) Bayesian analysis for randomized response models. Sankhyā B 61: 422–432
Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60: 63–69
Winkler RL, Franklin LA (1979) Warner’s randomized response model: a Bayesian approach. J Am Stat Assoc 74: 207–214
Wolfram S (2003) The Mathematica Book 5th ed. Wolfram Media
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Barabesi, L., Marcheselli, M. Bayesian estimation of proportion and sensitivity level in randomized response procedures. Metrika 72, 75–88 (2010). https://doi.org/10.1007/s00184-009-0242-7
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DOI: https://doi.org/10.1007/s00184-009-0242-7