Vol. 9, No. 2, 2016

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An optional unrelated question RRT model

Jeong S. Sihm, Anu Chhabra and Sat N. Gupta

Vol. 9 (2016), No. 2, 195–209

We propose a modified unrelated question randomized response technique (RRT) model which allows respondents the option of answering a sensitive question directly without using the randomization device if they find the question nonsensitive. This situation has been handled before by Gupta, Tuck, Spears Gill, and Crowe using the split sample approach. In this work we avoid the split sample approach, which requires larger total sample size. Instead, we estimate the prevalence of the sensitive characteristic by using an optional unrelated question RRT model, but the corresponding sensitivity level is estimated from the same sample by using the traditional binary unrelated question RRT model of Greenberg, Abul-Ela, Simmons, and Horvitz. We compare the simulation results of this new model with those of the split-sample based optional unrelated question RRT model of Gupta et al. and the simple unrelated question RRT model of Greenberg et al. Computer simulations show that the new binary response and quantitative response models have the smallest variance among the three models when they have the same sample size.

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optional randomized response models, unrelated questions randomized response models, parameter estimation, simulation study
Mathematical Subject Classification 2010
Primary: 62-02, 62-04, 62D05
Received: 21 November 2013
Accepted: 20 March 2014
Published: 2 March 2016

Communicated by Kenneth S. Berenhaut
Jeong S. Sihm
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
317 College Ave
Greensboro, NC 27412
United States
Anu Chhabra
Department of Mathematics
University of Delhi
Delhi 110052
Sat N. Gupta
Department of Mathematics and Statistics
University of North Carolina at Greensboro
317 College Ave
Greensboro, NC 27412
United States