A Modifed Forced Randomized Response Model

Authors

  • Adefemi Adeniran Augustine University Ilara-Epe
  • A. A. Sodipo Department of Statistics, University of Ibadan, Ibadan, Nigeria
  • C. G. Udomboso Department of Statistics, University of Ibadan, Ibadan, Nigeria

Keywords:

randomized response, proportion, sensitive group, maximum likelihood estimator, sampling distribution

Abstract

In this paper, we proposed a new Randomized Response Model (RRM) that estimate proportion of people in a population (P) belonging to a sensitive group (S) under study. Simple random sampling with replacement and strati?ed simple random sampling scheme were adopted. Maximum likelihood and Bayesian estimation procedures of the proposed model were developed and compared. The sampling distribution (expectation and variance) of the proposed estimator under the two sampling techniques, e?ciency comparison of the proposed model with some existing models, and numerical illustration of all the compared models were also explored. We found that the proposed model outperformed other existing RRMs in terms of e?ciency and it proved to be more protective in designing survey for sensitive related issues.

Dimensions

Amahia, G. N. (2010) Factors, prevention and correction methods for non-response in sample surveys. Central Bank of Nigeria, Journal of Applied Statistics, 1(1), 79-89.

Anscombe, F. J. (1962) Bayesian statistics, Journal of Royal Statistical Society, 25, 1-22.

Blair, G., Imai, K. and Zhou, Y-Y (2015) Design and Analysis of the Randomized Response Technique, Journal of the American Statistical Association, 110(511), 1304-1319, DOI: 10.1080/01621459.2015.1050028

Boruch, R. F. (1971) Assuring confidentiality of responses in social research: A note on strategies. The American Sociologist, 6(4), 308-311.

Bouza, C. N., Herrera, C. and Mitra, P. G. (2010) A review of randomized responses procedures: The qualitative variable case, Revista Investigaci´on, 31(3), 240-243.

Chong, A. C. Y., Chu. A. M. Y., So, M. K. P. and Chung, R. S. W. (2019) Asking Sensitive Questions Using the Randomized Response Approach in Public Health Research: An Empirical Study on the Factors of Illegal Waste Disposal, International Journal of Environmental and Public Health, 16, 1-15, doi:10.3390/ijerph16060970.

Cochran, W. G. (1977) Sampling Techniques, 3rd edition, New York: John Wiley and Sons, MR 0474575.

Diana, G., Riaz, S. and Shabbir, J. (2013) Hansen and Hurwitz estimator with scrambled response on the second call, Journal of Applied Statistics, 41(3), 596-611, http://dx.doi.org/10. 1080/02664763.2013.846305.

Elffers, H., Van Der Heijden, P. and Hezemans, M. (2003) Explaining regulatory noncompliance: A survey study of rule transgression for two dutch instrumental laws, applying the randomized response method, Journal of Quantitative Criminology, 19, 409-439, DOI: 10.1023/B:JOQC.0000005442.96987.9e.

Ewemooje, O. S. and Amahia, G. N. (2015) Improved Randomized Response Technique for Two Sensitive Attributes, Afrika Statistika, 10, 839-852, DOI: 10.16929/as/2015.639.78.

Fink, D. (1997) A compendium of conjugate priors: Environmental statistics group, Department of Biology, Montana state university Bozeman, MT 59717.

Fox, J. A. and Tracy, P. E. (1986), Randomized response: A method for sensitive surveys, Beverly Hills, CA: Sage.

Gingerich, D. W. (2010) Understanding off-the-books politics: conducting inference on the determinants of sensitive behavior with randomized response surveys, Political Analysis, 18, 349–380.

Greenberg, B. G., Abul-Ela, A. L., Simmons, W. R. and Horvitz, D. G. (1969) The unrelated question randomized response model: Theoretical framework, Journal of the American Statistical Association, 64(326), 520-539, https://doi.org/10.1080/01621459.1969.10500991.

Hong, K., Yum, J. and Lee, H. (1994) A stratified randomized response technique, The Korean Journal of Applied Statistics, 7, 141-147.

Hussain, Z., Shabbir, J. and Riaz, M. (2010) Bayesian estimation using Warner’s randomized response model through simple and mixture prior distributions, Communications in Statistics-Simulation and Computation, 40(1), 147-164, DOI: 10.1080/03610918.2010.532897, https://doi.org/10.1080/03610918.2010.532897.

Kim, J. M. and Warde, W. D. (2004) A stratified Warner’s randomized response model, Elsevier Journal of Journal of Statistical Planning and Inference, 120(1–2), 155–165.

Kim, J. M., Tebbs, J. M. and Seung-Won An (2006) Extensions of Mangat’s Randomizedresponse model, Elsevier Journal of Statistical Planning and Inference, 136(2006), 15541567.

Krumpal, I. (2012) Estimating the prevalence of xenophobia and anti-semitism in Germany: A comparison of randomized response and direct questioning, Social Science Research, 41, 1387-1403.

Lee, G. S., Hong, K. H., Kim, J. M. and Son, C. K. (2014) Estimation of the proportion of a sensitive attribute based on a two-stage randomized response model with stratified unequal probability sampling, Brazilian Journal of Probability and Statistics, 28(3), 381408, DOI:10.1214/12-BJP214.

Lensvelt-Mulders, G. J. L. M., Hox, J. J. and Van-der-Heijden, P. G. M. (2005) How to improve the efficiency of randomized response designs, Quality and Quantity: Springer (2005), 39, 253-265, DOI:10.1007/s11135-004-0432-3.

Mangat, N. S. and Singh, R. (1990) An alternative randomized response procedure. Biometrika, 77, 439-442, https://doi.org/10.1093/biomet/77.2.439.

Mangat, N. S. (1994) An improved randomized response strategy. Journal of Royal Statistical Society, Series B, 56(1), 93-95.

Quantember, A. (2009) A standardization of randomized response strategies, Survey Methodology, 35(2), 143-152, statistics canada, catalogue No.: 12-001X Business Survey Methods Division.

Rasinski, K. A., Willis, G. B., Baldwin, Yeh, W. C. and L. Lee, L. (1999) Methods of data collection, perceptions of risks and losses, and motivation to give truthful answers to sensitive survey questions, Applied Cognitive Psychology, 13, 465-484.

Rosenfeld, B., Imai, K. and Shapiro, J. (2015) An empirical validation study of popular survey methodologies for sensitive questions, American Journal of Political Science, 60(3), 783-802, doi: 10.1111/ajps.12205.

Stubbe, J. H., Chorus, A. M., Frank, L. E., Hon, O. and Heijden, P. G. (2014) Prevalence of Use of performance enhancing drugs by fitness centre members, Drug Testing and Analysis, 6, 434-438.

St-John, F. A., Keane, A. M., Edwards-Jones, G., Jones, L., Yarnell, R. W. and Jones, J. P. (2012) Identifying indicators of illegal behaviour: carnivore killing in human-managed landscapes, Proceedings of the Royal Society B: Biological Sciences, 279, 804-812.

Sudman, S. and Bradburn, N. M. (1982) Asking questions: A practical guide to questionnaire design, San Fransisco, CA: Jossey-Bass.

Usman, A. and Oshungade I. O. (2012) A mixed-stratified randomized response model for HIV seroprevalence surveys, Research Journal of Mathematics and Statistics, 4(3), 70-75.

Van der Heijden, P. G. M., Van Gils, G., Bouts, J. and Hox, J. J. (2000) A comparison of randomized response, computer-assisted self-interview, and face-to-face direct questioning, Sociological Methods and Research, 28, 505–537.

Warner, S. L. (1965) Randomized response: A survey technique for eliminating evasive answer bias, Journal of American Statistical Association, 60(309), 63-69, DOI: 10.2307/2283137, http://www.jstor.org/stable/2283137.

Winkler, R. L. and Franklin, L. A. (1979) Warner’s randomized response model: A Bayesian approach, Journal of the American Statistical Association, 74(365), 207-214, DOI: 10.2307/2286752, https://www.jstor.org/stable/2286752.

Zawar, H. and Khushnoor, K. (2013) On estimation of sensitive mean using scrambled data. World Applied Sciences Journal, 23(9), 1201-1206.

Published

2020-02-28

How to Cite

A Modifed Forced Randomized Response Model. (2020). Journal of the Nigerian Society of Physical Sciences, 2(1), 36-50. https://doi.org/10.46481/jnsps.2020.30

Issue

Volume 2, Issue 1, February 2020

Section

Original Research
Copyright & Licensing

Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A Modifed Forced Randomized Response Model. (2020). Journal of the Nigerian Society of Physical Sciences, 2(1), 36-50. https://doi.org/10.46481/jnsps.2020.30