Through algebraic and numerical comparisons, superiority ofthe proposed methodology is established.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this article, we use additive scrambling to estimate the mean of a sensitive variable.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:Through algebraic and numerical comparisons, superiority ofthe proposed methodology is established.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
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.
🔖
Cite This Article
ARSHAD, W., HUSSAIN, Z. (2022). On Generalized Additive Scrambled Response Modeling in Sensitive Surveys. Gazi University Journal of Science, Cilt: 32 - Sayı: 1, 372–383. https://ajindex.com/articles/521387
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).