Generating randomized response by inverse Bernoullian trials in unrelated characteristics model¹

Article type: Research Article

Authors: Chaudhuri, Arijit | Shaw, Purnima^*

Affiliations: Applied Statistics Unit, Indian Statistical Institute, Kolkata, India

Correspondence: [*] Corresponding author: Purnima Shaw, Reserve Bank of India, Bandra-Kurla Complex, Bandra (East), Mumbai-400041, India. E-mail:[email protected]

Note: [1] The views expressed in this paper are of the authors alone and not of the institution the corresponding author is working in that is the Reserve Bank of India and this applies to the corresponding author and not the first author.

Abstract: In estimating a finite population proportion of people bearing a stigmatizing characteristic Warner's (1965) Randomized Response (RR) device is well-known when the complementary characteristic is supposedly innocuous. But when both may be sensitive Simmons' Unrelated (URL, in brief) Model RR device is well-known as a feasible alternative. Both devices generate RR's by Bernoullian trials recording data on a match or mis-match of a respondent's true feature and the feature marked on a randomly chosen card drawn from a box placed in front of the person. A recently reported `alternative' device records instead the first occurrence of a `match' in repeatedly drawn cards from the box with replacement. This artifice fails with URL model. An amended procedure is presented demonstrating its advantages.

Keywords: Inverse RR, stigmatizing issues, unrelated model, varying probability sampling

DOI: 10.3233/MAS-160364

Journal: Model Assisted Statistics and Applications, vol. 11, no. 3, pp. 235-245, 2016