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Abstract
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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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Keywords
optional randomized response models, unrelated questions
randomized response models, parameter estimation,
simulation study
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Mathematical Subject Classification 2010
Primary: 62-02, 62-04, 62D05
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Milestones
Received: 21 November 2013
Accepted: 20 March 2014
Published: 2 March 2016
Communicated by Kenneth S. Berenhaut
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