On Generalized Additive Scrambled Response Modeling in Sensitive Surveys

In this article, we use additive scrambling to estimate the mean of a sensitive variable. In theproposed scrambling model, taking G (>1 ) as a positive integer chosen by the interviewer, eachrespondent is asked to randomly draw G values from a given distribution of scrambling variableand add average of these randomly drawn values to his/her true response on the sensitive variable.Using repetition of the scrambling experiment, we propose a relatively more efficient estimatorof sensitive mean without incurring any additional sampling cost. We present a generalization ofadditive scrambled response models and show that most of additive scrambling models are specialcases of suggested generalization. Through algebraic and numerical comparisons, superiority ofthe proposed methodology is established.

PDF

___

Warner, S. L., “Randomized response: a survey technique for eliminating evasive answer bias”, Journal of the American Statistical Association, 60:63-69, (1965).
Horvitz, D. G., Shah, B. V., Simmons, W. R., “The unrelated question randomized response model”, Proceedings of Socialogical Statistics Section of American Statistical Association, 65-72, (1967).
Greenberg, B. G., Abul-Ela Abdel-Latif, A., Simmons, W. R., Horvitz, D. G., “The unrelated question rr model: theoretical framework”, Journal of the American Statistical Association, 64: 52-539, (1969).
Greenberg, B.O., Kuebler, R. R. Jr., Abernathy, J. R., Horvitz, D. G., Application of the randomized response technique in obtaining quantitative data”, Journal of the American Statistical Association, 66:243-250, (1971).
Mangat, N. S., “An ımproved randomized response strategy”, Journal of the Royal Statistical Society Series B, 56: 93-95, (1994).
Singh, S., Joarder, A. H., “Unknown repeated trials in randomized response sampling”, Journal of Indian Society of Agricultural Statistics, 50(1): 103-105, (1997).
Gupta, S. N., Gupta, B. C., Singh, S., Estimation of sensitivity level of personal ınterview survey questions”, Journal of Statistical Planning and Inference, 100:239–247, (2002).
Arnab, R., “Optional randomized response techniques for complex survey designs”, Biometrical Journal, 46:114–124, (2004).
Mangat, N. S., Singh, R., Singh, S., “Violation of respondent’s privacy in moor’s model—ıts rectification through a random group strategy”, Communication in Statistics-Theory and Methods, 26:743–754, (1997).
Singh, S., Singh, R., Mangat. N. S., “Some alternative strategies to moor’s model in randomized response sampling- a survey technique for eliminating evasive answer bias”, Journal of Statistical Planning and Inference, 83: 243-255, (2002).
Chang, H. J., Huang, K. C., “Estimation of proportion and sensitivity of a qualitative character”, Metrika, 53:269-280, (2001).
Bhargava, M., Singh, R., “A modified randomization device for warner’s model”, Statistica, 60:315- 321, (2000).
Singh, S., Horn, S., Singh, R., Mangat, N. S., “On the use of modified randomization device for estimating the prevalence of a sensitive attribute”, Statistics in Transition, 6(4): 515-522, (2003).
Chang, H. J., Wang, C. L., Huang, K. C., “Using randomized response to estimate the proportion and truthful reporting probability in a dichotomous finite population”, Journal of Applied Statistics, 31:565-573, (2004).
Gupta, S. N., Thornton, B., Shabbir, J., Singhal, S, “A comparison of multiplicative and additive optional rrt models”, Journal of Statistical Theory and Application, 5:226-239, (2006).
Kim, J.M., Elam, M.E., “A Stratified Unrelated Randomized Response Model”, Statistical Papers, 48: 215–233, (2007).
Chaudhuri, A., Pal, S., “Estimating sensitive proportions from warner’s randomized responses in alternative ways restricting to only distinct units sampled”, Metrika, 68:147–156, (2008).
Huang, K. C., “Estimation for the sensitive characteristic using optional randomized response technique”, Quality and Quantity, 42:679-686, (2008).
Pal, S., “Unbiasedly estimating the total of a stigmatizing variable from complex survey on permitting options for direct or randomized responses”, Statistical Papers, 49: 157–164, (2008).
Diana, G. Perri, P. F., “Estimating a sensitive proportion through randomized response procedures based on auxiliary ınformation”, Statistical Papers, 50(3): 661–672, (2009).
Huang, K. C., “Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling”, Metrika, 71:341–352, (2010).
Himmelfarb, S., Edgell, S. E., “Additive constant model: a randomized response technique for eliminating evasiveness to quantitative response questions”, Psycholigical Bulletin, 87:525–530, (1980).
Gupta, S., Shabbir, J., Sehra, S., “Mean and Sensitivity Estimation in Optional Randomized Response Models”, Journal of Statistical Planning and Inference, 140(10): 2870-2874, (2010).
Mehta, S., Dass, B. K., Shabbir, J. and Gupta, S., “A three stage optional randomized response model, Journal of Statistical Theory and Practice, 6 (3): 417-427, (2012).
Gupta, S., Mehta, S., Shabbir, J., Dass, B. K., “Generalized scrambling in quantitative optional randomized response models”, Communications in Statistics - Theory and Methods, 42, 4034-4042, (2012).
Eichhron, B. H., Hayre, L. S., “Scrambled randomized response methods for obtaining sensitive quantitative data, Journal of Statistical Planning and Inference, 7:307–316, (1983).
Ryu, J. B., Kim, J. M., Heo, T. Y., Park, C. G., “On stratified randomized response sampling”, Model Assisted Statistics and Application,1:31–36, (2006).
Arcos, A., Rueda, M, D, M., Singh, S., “A generalized approach to randomised response for quantitative variables”, Quality & Quantity, 49:1239–1256, (2015).
Zaizai, Y., Wang, j., Lai, J., “An efficiency and protection degree-based comparison among the quantitative randomized response strategies, Communications in Statistics - Theory and Methods, 38:3, 400-408, (2008).
Hussain, Z., “On eliminating the scrambling variance in scrambled response models, International Journal of Academic Research in Business and Social Sciences, 2 (6), 39-45, (2012).