Estimating the proportion of non-heterosexuals in Taiwan using Christofides’ randomized response model: A comparison of different estimation methods

Investigating the Association of a Sensitive Attribute with a Random Variable Using the Christofides Generalised Randomised Response Design and Bayesian Methods

“…Based on the estimation method of Christofides (2003), the estimate of $$$ \theta $$$ may not fall in the parameter space $$$ \left[0,1\right] $$$. Thus, Hsieh and Perri (2021) proposed the Bayesian method combining the Gibbs sampling and MCMC to provide an estimate of $$$ \theta $$$ and ensure the estimate falls in this parameter space. This concept is extended to consider a model for the association between a sensitive attribute and a random variable under the GRR design of Christofides (2003).…”

“…The conditional distribution of $$$ {Y}_i $$$ given $$$ \theta $$$ and $$$ {D}_i={d}_i $$$ is then a Bernoulli distribution with probability $$$ p\left(\theta, {d}_i\right) $$$ of $$$ {Y}_i=L+1 $$$ and probability $$$ 1-p\left(\theta, {d}_i\right) $$$ of $$$ {Y}_i=0 $$$, denoted by $$$ {Y}_i\mid \theta, {D}_i={d}_i\sim \left(L+1\right)\times B\left(1,p\left(\theta, {d}_i\right)\right) $$$, $$$ i=1,2,\dots, n $$$, where $$$ B\left(1,p\right) $$$ denotes the Bernoulli distribution with probability $$$ p $$$ of success. Hence, Hsieh and Perri (2021) provided the Gibbs sampling procedure to estimate $$...$…”

“…) . However, in practice, through the GRR design of Christofides (2003), only Hsieh and Perri (2021) , n, where B(1, p) denotes the Bernoulli distribution with probability p of success. Hence, Hsieh and Perri (2021) provided the Gibbs sampling procedure to estimate 𝜃.…”

“…However, in practice, through the GRR design of Christofides (2003), only Hsieh and Perri (2021) , n, where B(1, p) denotes the Bernoulli distribution with probability p of success. Hence, Hsieh and Perri (2021) provided the Gibbs sampling procedure to estimate 𝜃. In this work, we utilise the concept of Hsieh and Perri (2021) to build up the Bayesian approach to estimate the parameters of a model for the association of a sensitive attribute with an auxiliary random variable of interest under the GRR design of Christofides (2003).…”

“…A validation study in Preisendörfer and Wolter (2014) showed that 42% (face‐to‐face interviews) and 33% (mail survey) of respondents did not admit that they had been convicted. In another real‐life situation, Hsieh and Perri (2021) pointed out the number of undesirable attribute individuals present in a community is generally underestimated if interviewees must answer sensitive questions directly. Thus, it is difficult to obtain reliable answers to the sensitive questions through direct questioning.…”