Bayes Linear Estimators for Randomized Response Models

原文摘要

Bayes linear estimators provide simple Bayesian methods and require a minimum of prior specification. In this article, Bayes linear estimators are derived for a variety of randomized response models. Randomized response aims to reduce false responses on sensitive questions, at the expense of some loss of information in each observation. In this context, Bayesian methods are attractive because they permit the incorporation of potentially useful prior information. The basic principle of randomized response is that an interviewee answers one of two or more different questions, depending on the outcome of some randomizing device. The interviewer does not know which question has been answered. In this way, it is hoped, the interviewee will feel able to answer sensitive questions honestly, where direct questioning might have produced false responses. Two versions of randomized response are examined: the original formulation of Warner (1965) and the unrelated question method of Simmons (Horvitz, Shah, and Simmons 1967). Other Bayesian analyses of these models have been proposed by Winkler and Franklin (1979) and Pitz (1980), respectively, using parametric models of prior information. Using the Bayes linear estimator, generally similar results are obtained from a nonparametric model. This model extends the applicability of the Bayesian approach, while also offering estimates that are trivial to compute.

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