Warner's Randomized Response Model: A Bayesian Approach

Winkler, Robert L.; Franklin, LeRoy A.

doi:10.2307/2286752

Cited by 19 publications

(16 citation statements)

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“…Combining and , the posterior density is given by where π k ≥ 0 for k ∈{1, … , K }, and . For K = 2, the posterior density given by is equal to the density given in Winkler & Franklin (1979). The case for which p 11 = p 22 = ?…”

Section: The Standard Randomized Response Modelmentioning

confidence: 99%

“…The prior density is non‐conjugate and the posterior density is not a standard density. Migon & Tachibana (1997) and Winkler & Franklin (1979) provide approximations of the density for the case K = 2. Unnikrishnan & Kunte (1999) use a Metropolis–Hastings algorithm within a Gibbs sampler for the generalized Warner model where K > 2.…”

Section: The Standard Randomized Response Modelmentioning

confidence: 99%

“…Second, model selection between non‐nested models is intuitively handled by looking at Bayes factors (Newton & Raftery 1994). Bayesian inference concerning probability estimation given the standard RR design is presented in Migon & Tachibana (1997), Unnikrishnan & Kunte (1999) and Winkler & Franklin (1979). Bayesian inference concerning an RR item‐response model is discussed in Fox (2005).…”

Section: Introductionmentioning

confidence: 99%

“…Bayesian inference concerning an RR item‐response model is discussed in Fox (2005). The discussion in the current paper will use the approach in Winkler & Franklin (1979), although the formulation of the posterior density is slightly more general. There is a close link here with the literature on Bayesian inference regarding misclassified data; see, for example, Viana (1994).…”

Section: Introductionmentioning

confidence: 99%

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Accounting for Non‐compliance in the Analysis of Randomized Response Data

Hout¹,

Klugkist

2009

Aus NZ J of Statistics

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The randomized response model is a misclassification design that is used to protect the privacy of respondents with respect to sensitive questions. Conditional misclassification probabilities are specified by the researcher and are therefore considered to be known. It is to be expected that some of the respondents do not comply with respect to the misclassification design. These respondents induce extra perturbation, which is not accounted for in the standard randomized response model. An extension of the randomized response model is presented that takes into account assumptions with respect to non-compliance under simple random sampling. The extended model is investigated using Bayesian inference. The research is motivated by randomized response data concerning violations of regulations for social benefit.

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Section: The Standard Randomized Response Modelmentioning

confidence: 99%

Section: The Standard Randomized Response Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accounting for Non‐compliance in the Analysis of Randomized Response Data

Hout¹,

Klugkist

2009

Aus NZ J of Statistics

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“…Nonetheless, attempts have been made on the Bayesian analysis of RRTs. For example, Winkler and Franklin (1979) gave an approximate Bayesian analysis of Warner's mirrored design, O'Hagan (1987) derived Bayesian linear estimators for the unrelated question design, and Oh (1994) used data augmentation to introduce latent variables to Gibbs sampling of the mirrored design, the unrelated question design and the two-stage design with binary and polychotomous responses. van den Hout and Klugkist (2009) proposed Bayesian inference that takes into account assumptions with respect to non-compliance under simple random sampling.…”

Section: Review Of Randomised Response Designsmentioning

confidence: 99%

Bayesian Analysis of a Sensitive Proportion for a Small Area

Nandram

2018

Int Statistical Rev

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Summary Without accounting for sensitive items in sample surveys, sampled units may not respond (nonignorable nonresponse) or they respond untruthfully. There are several survey designs that address this problem and we will review some of them. In our study, we have binary data from clusters within small areas, obtained from a version of the unrelated‐question design, and the sensitive proportion is of interest for each area. A hierarchical Bayesian model is used to capture the variation in the observed binomial counts from the clusters within the small areas and to estimate the sensitive proportions for all areas. Both our example on college cheating and a simulation study show significant reductions in the posterior standard deviations of the sensitive proportions under the small‐area model as compared with an analogous individual‐area model. The simulation study also demonstrates that the estimates under the small‐area model are closer to the truth than for the corresponding estimates under the individual‐area model. Finally, for small areas, we discuss many extensions to accommodate covariates, finite population sampling, multiple sensitive items and optional designs.

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