Abstract
This chapter is devoted entirely to randomized response techniques which can be implemented to estimate certain parameters of a qualitative stigmatizing characteristic. Descriptions of the randomized response procedures of specific techniques are given. In particular details are provided for Warner’s, Simmon’s, Kuk’s, Christofides’, and the Forced Response randomized response techniques. For those techniques, explicit formulae are given for the various estimators of interest and measures of their accuracy, assuming that the sample is chosen according to a general sampling design. However, given that most practitioners are more familiar with simple random sampling without replacement, the formulae are explicitly stated for this particular sampling scheme as well. In addition to the numerous randomized response techniques reviewed, this chapter includes a recently developed randomized response technique which uses the Poisson distribution to estimate parameters related to a stigmatizing characteristic which is extremely rare. Furthermore, we discuss an approach using the geometric distribution to generate randomized responses. Also in this chapter, techniques dealing with multiple sensitive characteristics are described. Finally, some aspects of the Bayesian approach in analyzing randomized response data are presented along with a brief literature review on the topic.
Keywords
- Maximum Likelihood Estimator
- Unbiased Estimator
- Simple Random Sampling
- Identical Card
- Sensitive Characteristic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alhassan, A.W., Ohuchi, S., Taguri, M. (1991). Randomized response designs considering the probability of dishonest answers. Journal of the American Statistical Association, 4, 1–24.
Arnab, R. (2004). Optional randomized response techniques for complex survey designs. Biometrical Journal, 46, 114–124.
Bar-Lev, S.K., Bobovitch, E., Boukai, B. (2003). A common conjugate prior structure for several randomized response models. Test, 12, 101–113.
Barabesi, L., Franceschi, S., Marcheselli, M. (2012). A randomized response procedure for multiple sensitive questions. Statistical Papers, 53, 703–718.
Barabesi, L., & Marcheselli, M. (2006). A practical implementation and Bayesian estimation in Franklin’s randomized response procedure. Communication in Statistics- Simulation and Computation, 35, 563–573.
Barabesi, L., & Marcheselli, M. (2010). Bayesian estimation of proportion and sensitivity level in randomized response procedures. Metrika, 72, 75–88.
Basu, D. (1969). Role of the sufficiency and likelihood principles in sample survey theory. Sankhya, Series A, 31, 441–454.
Boruch, R.F. (1972). Relations among statistical methods for assuring confidentiality of social research data. Social Science Research, 1, 403–414.
Bourke, P.D. (1981). On the analysis of some multivariate randomized response designs for categorical data. Journal of Statistical Planning and Inference, 5, 165–170.
Chang, H.-J., Wang, C.-L., Huang, K.-C. (2004). Using randomized response to estimate the proportion and truthful reporting probability in a dichotomous finite population. Journal of Applied Statistics, 31, 565–573.
Chaudhuri, A. (2001a). Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population. Journal of Statistical Planning and Inference, 94, 37–42.
Chaudhuri, A. (2001b). Estimating sensitive proportions from unequal probability samples using randomized responses. Pakistan Journal of Statistics, 17, 259–270.
Chaudhuri, A. (2002). Estimating sensitive proportions from randomized responses in unequal probability sampling. Calcutta Statistical Association Bulletin, 52, 315–322.
Chaudhuri, A. (2004). Christofides’ randomized response technique in complex surveys. Metrika, 60, 223–228.
Chaudhuri, A. (2010). Essentials of survey sampling. New Delhi: Prentice Hall of India.
Chaudhuri, A. (2011). Randomized response and indirect questioning techniques in surveys. Boca Raton: Chapman & Hall, CRC Press, Taylor & Francis Group.
Chaudhuri, A., Adhikary, A.K., Dihidar, S. (2000). Mean square error estimation in multi-stage sampling. Metrika, 52, 115–131.
Chaudhuri, A., & Mukerjee, R. (1988). Randomized response: theory and techniques. New York: Marcel Dekker.
Chaudhuri, A., & Saha, A. (2005). Optional versus compulsory randomized response techniques in complex surveys. Journal of Statistical Planning and Inference, 135, 516–527.
Christofides, T.C. (2003). A generalized randomized response technique. Metrika, 57, 195–200.
Christofides, T.C. (2005a). Randomized response in stratified sampling. Journal of Statistical Planning and Inference, 128, 303–310.
Christofides, T.C. (2005b). Randomized response technique for two sensitive characteristics at the same time. Metrika, 62, 53–63.
Cruyff, M.J.L.F., Bockenholt, U., van der Hout, A., van der Heijden, P.G.M. (2008). Accounting for self-protective responses in randomized response data from social security survey using the zero-inflated Poisson model. Annals of Applied Statistics, 2, 316–331.
Dalenius, T., & Vitale, R.A. (1974). A new RR design for estimating the mean of a distribution. Technical Report, No 78, Brown University, Providence, RI.
Devore, J.L. (1977). A note on the randomized response technique. Communications in Statistics - Theory and Methods, 6, 1525–1529.
Ericson, W.A. (1969). Subjective Bayesian models in sampling finite populations. Journal of the Royal Statistical Society: Series B, 31, 195–233.
Fligner, M.A., Policello, G.E., Singh, J. (1977). A comparison of two survey methods with consideration for the level of respondent protection. Communications in Statistics - Theory and Methods, 6, 1511–1524.
Fox, J.A., & Tracy, P.E. (1986). Randomized response: a method for sensitive surveys. London: Sage.
Franklin, L.A. (1989). A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Communications in Statistics - Theory and Methods, 18, 489–505.
Gelfand, A.E., & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
Godambe, V.P. (1955). A unified theory of sampling from finite populations. Journal of the Royal Statistical Society: Series B, 17, 269–278.
Greenberg, B.G., Abul-Ela, A.-L.A., Simmons, W.R., Horvitz, D.G. (1969). The unrelated question RR model: theoretical framework. Journal of the American Statistical Association, 64, 520–539.
Gupta, S., & Shabbir, J. (2007). On the estimation of population mean and sensitivity in two-stage optional randomized response model. Journal of the Indian Society of Agricultural Statistics, 61, 164–168.
Gupta, S., Shabbir, J., Sehra, S. (2010). Mean and sensitivity estimation in optional randomized response models. Journal of Statistical Planning and Inference, 140, 2870–2874.
Hastings, W.K. (1970). Monte Carlo sampling methods using Markov Chains and their applications. Biometrika, 57, 97–109.
Hong, K., Yum, J., Lee, H. (1994). A stratified randomized response technique. Korean Journal of Applied Statistics, 7, 141–147.
Horvitz, D.G., Shah, B.V., Simmons, W.R. (1967). The unrelated question RR model. Proceedings of the Social Statistics Section of the American Statistical Association (pp. 65–72). Alexandria, VA: ASA.
Horvitz, D.G., & Thompson, D.J. (1952). A generalization of sampling without replacement from finite universe. Journal of the American Statistical Association, 47, 663–685.
Huang, K.-C. (2004). A survey technique for estimating the proportion and sensitivity in a dichotomous finite population. Statistica Neerlandica, 58, 75–82.
Huang, K.-C. (2008). Estimation for sensitive characteristics using optional randomized response technique. Quality and Quantity, 4, 679–686.
Hussain, Z., & Shabbir, J. (2009). Bayesian estimation of population proportion of a sensitive characteristic using simple beta prior. Pakistan Journal of Statistics, 25, 27–35.
Kim, J.-M., & Elam, M.E. (2007). A stratified unrelated question randomized response model. Statistical Papers, 48, 215–233.
Kim, J.-M., & Heo, T.-Y. (2013). Randomized response group testing model. Journal of Statistical Theory and Practice, 7, 33–48.
Kim, J.-M., Tebbs, J.M., An, S.-W. (2006). Extensions of Mangat’s randomized response model. Journal of Statistical Planning and Inference, 136, 1554–1567.
Kim, J.-M., & Warde, W.D. (2004). A stratified Warner’s randomized response model. The Journal of Statistical Planning and Inference, 120, 155–165.
Kuk, A.Y.C. (1990). Asking sensitive questions indirectly. Biometrika, 77, 436–438.
Lakshmi, D.V., & Raghavarao, D. (1992). A test for detecting untruthful answering in randomized response procedures. Journal of Statistical Planning and Inference, 31, 387–390.
Land, M., Singh, S., Sedory, S.A. (2012). Estimation of a rare sensitive attribute using Poisson distribution. Statistics, doi: 10.1080/02331888.2010.524300.
Lee, C.-S., Sedory, S.A., Singh, S. (2013). Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. Statistics and Probability Letters, 83, 399–409.
Lee, G.-S., Uhm, D., Kim, J.-M. (2012). Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics, doi:10.1080/02331888.2011.625503.
Liu, P.T., Chow, L.P., Mosley, W.H. (1975). Use of RR technique with a new randomizing device. Journal of the American Statistical Association, 70, 329–332.
Mangat, N.S. (1991). An optional randomized response sampling technique using nonstigmatized attribute. Statistics, 51, 595–602.
Mangat, N.S. (1992). Two stage randomized response sampling procedure using unrelated question. Journal of the Indian Society of Agricultural Statistics, 44, 82–87.
Mangat, N.S. (1994). An improved randomized response strategy. Journal of the Royal Statistical Society: Series B, 56, 93–95.
Mangat, N.S., & Singh, R. (1990). An alternative randomized response procedure. Biometrika, 77, 439–442.
Mangat, N.S., Singh, R., Singh, S. (1992). An improved unrelated question randomized response strategy. Calcutta Statistical Association Bulletin, 42, 277–281.
Mangat, N.S., & Singh, S. (1994). An optional randomized response sampling technique. Journal of the Indian Statistical Association, 32, 71–75.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.
Migon, H.S., & Tachibana, V.M. (1997). Bayesian approximations in randomized response model. Computational Statistics and Data Analysis, 24, 401–409.
Moshagen, M., & Musch, J. (2011). Surveying multiple sensitive attributes using an extension of the randomized response technique. International Journal of Public Opinion Research, doi:10.1093/ijpor/edr034.
O’Hagan, A. (1987). Bayes linear estimators for randomized response models. Journal of the American Statistical Association, 82, 580–585.
Pitz, G.F. (1980). Bayesian analysis of random response models. Psychological Bulletin, 87, 209–212.
Rao, J.N.K., Hartley, H.O., Cochran, W.G. (1962). On the simple procedure of unequal probability sampling without replacement. Journal of the Royal Statistical Society: Series B, 24, 482–491.
Saha, A. (2011). An optional scrambled randomized response technique for practical surveys. Metrika, 73, 139–149.
Singh, S., & Grewal, I.S. (2013). Geometric distribution as a randomization device: implemented to the Kuk’s model. International Journal of Contemporary Mathematical Sciences, 8, 243–248.
Singh, S., & Joarder, A.H. (1997a). Unknown repeated trials in randomized response sampling. Journal of the Indian Statistical Association, 30, 109–122.
Singh, S., & Joarder, A.H. (1997b). Optional randomized response technique for sensitive quantitative variable. Metron, 55, 151–157.
Tamhane, A.C. (1981). Randomized response techniques for multiple sensitive attributes. Journal of the American Statistical Association, 76, 916–923.
Tierney, L., & Kadane, J.B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81, 82–86.
Unnikrishnan, N.K., & Kunte, S. (1999). Bayesian analysis for randomized response models. Sankhya Series B, 61, 422–432.
Walpole, R.E., & Myers, R.H. (1993). Probability and statistics for engineers and scientists, 5th edn. Englewood Cliffs, NJ: Prentice-Hall.
Warner, S.L. (1965). Randomized Response: a survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60, 63–69.
Winkler, R.L., & Franklin, L.A. (1979). Warner’s randomized response model: a Bayesian approach. Journal of the American Statistical Association, 74, 207–214.
Yates, F., & Grundy, P.M. (1953). Selection without replacement from within strata with probability proportional to size. Journal of the Royal Statistical Society: Series B, 15, 253–261.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chaudhuri, A., Christofides, T.C. (2013). Randomized Response Techniques to Capture Qualitative Features. In: Indirect Questioning in Sample Surveys. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36276-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-36276-7_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36275-0
Online ISBN: 978-3-642-36276-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)