Warner's Randomized Response Model: A Bayesian Approach

Winkler, Robert L.; Franklin, LeRoy A.

doi:10.1080/01621459.1979.10481639

Cited by 57 publications

(32 citation statements)

References 6 publications

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“…Further analyses are straightforward, given the sampled parameter values. This in contrast to earlier work on Bayesian inference of randomized response data that results in posterior distributions that are not easy to work with, involves heavy computations, or rely on approximations (see, e.g., Migon & Tachibana, 1997;Winkler & Franklin, 1979). The implementation of the MCMC algorithm can be extended to perform certain model checks.…”

Section: Discussionmentioning

confidence: 89%

Randomized Item Response Theory Models

Fox

2005

Journal of Educational and Behavioral Statistics

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The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR Keywords: analysis of variance, item response theory model, Markov chain Monte Carlo (MCMC), random effects, randomized responseThe collection of data through surveys on highly personal and sensitive issues may lead to answering refusals and false responses, making inferences difficult. Obtaining valid and reliable information depends on the cooperation of the respondents, and the willingness of the respondents depends on the confidentiality of their responses. Warner (1965) developed a data collection procedure, the randomized response (RR) technique, that allows researchers to obtain sensitive information while guaranteeing privacy to respondents. For example, a randomizing device is used to select a question from a group of questions and the respondent answers the selected question. The respondent is protected because the interviewer will not know which question is being answered. Warner's and related approaches were specifically developed to hide answers of the respondents and to estimate proportions and related confidence intervals in the population.In some applications, randomized response data can be hierarchically structured, and there is an interest in group differences regarding some sensitive individual characteristic. One could think of an application where it is of interest to know if cheating behavior differs across faculties or if social security fraud is more likely to appear in groups with certain characteristics. However, the usual randomized response models do not allow a hierarchical data analysis of the RR data. Statistical methods for hierarchically structured data, for example analysis of variance (ANOVA) or multilevel analysis, cannot be applied because the true individual

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Section: Discussionmentioning

confidence: 89%

Randomized Item Response Theory Models

Fox

2005

Journal of Educational and Behavioral Statistics

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“…van der Heijden and van Gils (1996) developed a similar likelihood framework for the forced response and disguised response designs. Additionally, Warner (1965) considered the linear regression model while Winkler and Franklin (1979) and O'Hagan (1987) explored its Bayesian extensions. …”

Section: Multivariate Regression Modelmentioning

confidence: 99%

E-research – selected issues concerning the Internet attitudes and opinions research

Kulikowski¹

2015

e-mentor

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About a half century ago, in 1965, Warner proposed the randomized response method as a survey technique to reduce potential bias due to nonresponse and social desirability when asking questions about sensitive behaviors and beliefs. This method asks respondents to use a randomization device, such as a coin flip, whose outcome is unobserved by the interviewer. By introducing random noise, the method conceals individual responses and protects respondent privacy. While numerous methodological advances have been made, we find surprisingly few applications of this promising survey technique. In this article, we address this gap by (1) reviewing standard designs available to applied researchers, (2) developing various multivariate regression techniques for substantive analyses, (3) proposing power analyses to help improve research designs, (4) presenting new robust designs that are based on less stringent assumptions than those of the standard designs, and (5) making all described methods available through open-source software. We illustrate some of these methods with an original survey about militant groups in Nigeria.

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“…Song and Kim [34] proposed the Bayes estimator of a rare attribute using RRT, and showed that their Bayes estimator was robust to priors. Now, by considering the Winkler and Franklin's [17] idea of identifying prior information and analyzing the posterior distribution (as done by Hussain et al [32]), we proposed to study a general class of RRTs yielding and eliciting the probability of a yes response given as follows: P (yes) = = c A + g; (1) where c and g are RRT-dependent real numbers, A is the true, yet known, population proportion of individuals with sensitive traits.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the Bayesian technique provides a normal way to study and deduce situations such as randomized response sampling where only limited information is available. Although the Bayesian analysis of RRTs has been studied, only a few attempts have been made in this area, e.g., Winkler and Franklin [17], Migon and Tachibana [18], Pitz [19], O'Hagan [20], Spurrier and Padgett [21], Oh [22], Unnikrishnan and Kunte [23], Barabesi and Marcheselli [24,25], Hussain and Shabbir [26][27][28], Hussain et al [29], and Bar-Lev et al [30].…”

Section: Introductionmentioning

confidence: 99%

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Investigating the Impact of Simple and Mixture Priors on Estimating Sensitive Proportion Through a General Class of Randomized Response Models

et al. 2018

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Abstract. Randomized response is an e ective survey method to collect subtle information. It facilitates responding to over-sensitive issues and defensive questions (such as criminal behavior, gambling habits, drug addictions, abortions, etc.) while maintaining con dentiality. In this paper, we conducted a Bayesian analysis of a general class of randomized response models by using di erent prior distributions, such as Beta, Uniform, Je reys, and Haldane, under squared error loss, and precautionary and DeGroot loss functions. We have also expanded our proposal to the case of mixture of Beta priors under squared error loss function. The performance of the Bayes and maximum likelihood estimators has been evaluated in terms of mean squared errors. Moreover, an application with real dataset has been also provided to explain the proposal for practical considerations.

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Warner's Randomized Response Model: A Bayesian Approach

Cited by 57 publications

References 6 publications

Randomized Item Response Theory Models

Randomized Item Response Theory Models

E-research – selected issues concerning the Internet attitudes and opinions research

Investigating the Impact of Simple and Mixture Priors on Estimating Sensitive Proportion Through a General Class of Randomized Response Models

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