Randomized Response Technique Model Research Articles

A Mixture Quantitative Randomized Response Model That Improves Trust in RRT Methodology

The Quantitative Randomized Response Technique (RRT) can be used by researchers to obtain honest answers to questions that, due to their sensitive (socially undesirable, dangerous, or even illegal) nature, might otherwise invoke partially or completely falsified responses. Over the years, Quantitative RRT models, sometimes called Scrambling models, have been developed to incorporate such advancements as mixture, optionality and enhanced trust, each of which has important benefits. However, no single model incorporates all of these features. In this study, we propose just such a unified model, which we call the Mixture Optional Enhanced Trust (MOET) model. After developing methodologies to assess MOET based on standard approaches and using them to explore the key characteristics of the new model, we show that MOET has superior efficiency compared to the Quantitative Optional Enhanced Trust (OET) model. We also show that use of the model’s mixture capability allows practitioners to optimally balance the model’s efficiency with its privacy, making the model adaptable to a wide variety of research scenarios.

Kernel density estimation using additive randomized response technique (RRT) models

In 2002 Ahmad (Ahmad 2002) introduced the kernel density estimation of the density curve of a sensitive variable based on multiplicative RRT models and provided some theoretical results. In this article, we propose a kernel density estimator in the context of additive RRT models, which are more commonly used in the field of survey sampling. A simulation study is presented to validate the theoretical results from the previous work of Ahmad (Ahmad 2002), and also compare the performances of the kernel density estimators based on the additive and multiplicative RRT models. Simulations show that the proposed kernel density estimator using additive scrambling performs better than the one using multiplicative scrambling, and it allows more error in the bandwidth selection in kernel density estimation.

Mitigating lack of trust in quantitative randomized response technique models

Social Desirability Bias (SDB) often leads to low response rate or worse, untruthful responding during face-to-face surveys involving sensitive questions. Randomized Response Technique (RRT) is often used to circumvent SDB by allowing respondents to provide a scrambled response. However, if respondents do not trust the RRT model, significant bias can still be introduced in the estimates. Yet, none of the quantitative RRT models currently account for respondents’ lack of trust. We propose an Optional Enhanced Trust (OET) quantitative RRT model that mitigates the effect of respondents’ lack of trust by allowing respondents who do not trust the traditional additive RRT model to use an alternative scrambling technique. Using a combined measure of respondent privacy and model efficiency, we demonstrate both theoretically and empirically that the proposed OET model is superior to the traditional Warner’s model.

A Two-Stage Unrelated Question Randomized Response Model for Estimating the Prevalence of Stigmatized Attribute

The randomized response technique (RRT) is an effective method designed to obtain the stigmatized information from respondents while assuring the privacy. In this study, we propose a new two-stage unrelated question RRT model to estimate the prevalence of sensitive attribute π when the proportion of unrelated innocuous attribute is known and unknown. A simulation study is carried out to validate the theoretical results of proposed estimators. The utility of proposed two-stage unrelated question RRT model under stratification is also explored. An efficiency comparison between the proposed two-stage unrelated question RRT model and the Singh and Suman RRT model is carried out numerically under simple and stratified random sampling.

An Improved Two-stage Randomized Response Model for Estimating the Proportion of Sensitive Attribute

The randomized response technique (RRT) is an effective method designed to obtain the stigmatized information from respondents while assuring the privacy. In this study, we propose a new two-stage RRT model to estimate the prevalence of sensitive attribute ([Formula: see text]). A simulation study shows that the empirical mean and variance of proposed estimator are close to corresponding theoretical values. The utility of proposed two-stage RRT model under stratification is also explored. An efficiency comparison between proposed two-stage RRT model and some existing RRT models is carried out numerically under simple and stratified random sampling.

A mixture binary RRT model with a unified measure of privacy and efficiency

In this study, we introduce a mixture binary Randomized Response Technique (RRT) model by combining the elements of the Greenberg Unrelated Question model and the Warner Indirect Question model. We also account for untruthful responding in the proposed model. A unified measure of model efficiency and respondent privacy is also presented. Finally, we present a simulation study to validate the theoretical findings.

Mean estimation with generalized scrambling using two-phase sampling

Sousa et al. and Gupta et al. presented ratio and regression estimators of population mean of a sensitive variable using auxiliary information in simple random sampling without replacement. In this article, we propose a generalized randomized response technique (RRT) model and use it to develop some exponential estimators in two-phase sampling. We also discuss the privacy protection level of the proposed RRT model. Theoretical and empirical results are presented to examine the performance of the proposed mean estimators in relation to other mean estimators.

A two-stage unrelated question randomized response model for estimating the rare sensitive parameter under Poisson distribution

In this paper, we propose a new two-stage unrelated question randomized response technique (RRT) model to estimate the mean of the number of persons possessing a rare sensitive attribute using the Poisson distribution. The utility of proposed two-stage unrelated question RRT model under stratification is also explored. Efficiency comparison between proposed two-stage unrelated question and Singh and Suman (2019) RRT model is carried out numerically under simple random sampling, and with Suman and Singh (2019) in stratified random sampling, respectively.

Bayesian analysis of optional unrelated question randomized response models

The randomized response technique (RRT) is an effective method designed to obtain the sensitive information from respondents while assuring the privacy. Narjis and Shabbir [Narjis, G., and J. Shabbir. 2018. Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques. Communications in Statistics – Simulation and Computation 0 (0):1–15] proposed three binary optional unrelated question RRT models for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In this study, we have developed the Bayes estimators of two parameters for optional unrelated question RRT model along with their corresponding minimal Bayes posterior expected losses (BPEL) under squared error loss function (SELF) using beta prior. Relative losses, mean squared error (MSE) and absolute bias are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Narjis and Shabbir (2018). A real survey data are provided for practical utilizations.

Estimating Prevalence of Sensitive Attribute with Optional Unrelated Question Randomized Response Models under Simple and Stratified Random Sampling

In this study, we propose optional randomized response technique (RRT) models in binary response situation. The utility of proposed optional RRT models under stratification are also explored. Gupta et al.cite{Singh} introduced an ingenious idea of optional RRT model, that a question may be sensitive for one respondent but may not be sensitive for another. This study focus on estimating $ pi $, the prevalence of sensitive attribute, $ omega $, the sensitivity level of the underlying sensitive question when the proportion of unrelated innocuous attribute $ pi_{{x}} $ is unknown. A new multi-question approach are proposed and used for estimation of parameters $ (pi,omega) $. A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically under simple and stratified random sampling.

Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques

In this study, we propose optional randomized response technique (RRT) models in binary response situation. Gupta, Gupta, and Singh (2002) introduced the basic premise of optional RRT model, that a question may be sensitive for one respondent but may not be sensitive for another. In an optional RRT model, a respondent is requested to provide a scrambled response only if he/she considers the question is sensitive. Otherwise, the respondent provides a truthful response. This study focus on estimating π, the prevalence sensitive characteristics, and ω, the sensitivity level of the underlying sensitive question. Two-question and split-sample approaches are used for parameters estimation. A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically.

Examining conservation compliance with randomized response technique analyses.

Understanding violations of laws or social norms designed to protect natural resources from overexploitation is a priority for conservation research and management. Because direct questioning about stigmatized behaviors can produce biased responses, researchers have adopted more complex, indirect questioning techniques. The randomized response technique (RRT) is one of the most powerful indirect survey methods, yet analyses of these data require sophisticated statistical models. To date, there has been limited user-friendly software to analyze RRT data, particularly for models that combine information from multiple RRT questions. We developed an R package, zapstRR (ZoologicAl Package for RRT) that provides functions for 3 RRT models that can be applied to single or multiple RRT questions. With these functions, researchers can estimate the prevalence of conservation noncompliance, determine the number of violations by individuals, perform regressions for univariate and multivariate RRT data, and correct prevalence estimates for evasive-response bias. We illustrate the use of these estimators for RRT data through an examination of 2 case studies: illegal bird hunting where the interview consisted of a standard RRT question design and a novel implementation designed to offer further anonymity to respondents and reveal the impact of educational interventions on illegal bushmeat consumption. The case studies demonstrate how the models can work in tandem to uncover distinct patterns within RRT data sets. The case studies also show how several assumptions are central to the application of the multivariate models.

Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model

ABSTRACTSihm et al. (2016) proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. (2016). The results obtained are illustrated with the help of real survey data using non informative prior.

A unified measure of respondent privacy and model efficiency in quantitative RRT models

Model efficiency and respondent privacy are two important considerations while comparing two randomized response technique (RRT) models. Either the model efficiency level is kept fixed and the model offering greater privacy is preferred, or the privacy level is kept fixed and we prefer the model with better efficiency. In our current work, we propose a unified measure of model quality for a quantitative RRT model and compare several competing models with respect to this measure.

An optional unrelated question RRT model

We propose a modified unrelated question randomized response technique (RRT) model which allows respondents the option of answering a sensitive question directly without using the randomization device if they find the question nonsensitive. This situation has been handled before by Gupta, Tuck, Spears Gill, and Crowe using the split sample approach. In this work we avoid the split sample approach, which requires larger total sample size. Instead, we estimate the prevalence of the sensitive characteristic by using an optional unrelated question RRT model, but the corresponding sensitivity level is estimated from the same sample by using the traditional binary unrelated question RRT model of Greenberg, Abul-Ela, Simmons, and Horvitz. We compare the simulation results of this new model with those of the split-sample based optional unrelated question RRT model of Gupta et al. and the simple unrelated question RRT model of Greenberg et al. Computer simulations show that the new binary response and quantitative response models have the smallest variance among the three models when they have the same sample size.

A Two-stage Binary Optional Randomized Response Model

Social desirability bias (SDB) is the tendency in respondents to answer questions untruthfully in the hope of giving good impression to others. SDB occurs when the survey question is highly sensitive or personal. The Randomized Response Technique (RRT) is one of several methods to get around SDB in face-to-face interview surveys involving sensitive questions. In this article, we first review some of the existing binary response RRT models. Then, we propose a new model—Two-Stage Binary Optional RRT model. Much of the focus is on estimating π, the prevalence of sensitive characteristic, and ω, the sensitivity level of the underlying question. We discuss the asymptotic properties of our estimators and present some simulation results. It turns out that the proposed Two-Stage Binary Optional RRT model is more effective than the Optional RRT model proposed by Gupta (2001).

Surveying Multiple Sensitive Attributes using an Extension of the Randomized-Response Technique

Surveying Multiple Sensitive Attributes using an Extension of the Randomized-Response Technique

Mean and sensitivity estimation in optional randomized response models

Optional randomized response models were introduced by Gupta et al. (2002). These models are based on the basic premise that a question may be sensitive for one respondent but may not be sensitive for another. In an optional RRT (randomized response technique) model, a respondent is asked to provide a scrambled response only if the respondent considers the question sensitive. Otherwise, the respondent provides a truthful response. The researcher does not know which type of response is provided. The proportion of respondents who provide a scrambled response is known as the sensitivity level of the question. In this paper, we estimate simultaneously the mean and the sensitivity level of a quantitative-response sensitive question using a two stage optional RRT model. The estimators are unbiased and asymptotically normally distributed. We discuss the advantages and disadvantages of using additive and multiplicative scrambling.

Note On "the Randomized Response Approach"

This addendum updates Fox and Tracy's (1980) summary of work on the randomized response technique (RRT). It notes the recent development of an additive constants model for sensitive questions that require a numerical response. It further calls the reader's attention to the possibility of correlational research using RRT models by presenting the derivation of the correlation and correction for attentuation between two variables measured by the additive constants model and by noting a paper that does the same for several other RRT models.

The Efficiency of the Multiple Trial Randomized Response Technique

It has been proven theoretically that repeated administration of two-related-question randomized response technique (RRT) substantially increases the efficiency by reducing the variance of the estimate. The realtive efficiency of RRT to direct question with various number of trials per respondent under various degrees of truthful response and various conditions has also been examined. However, if the respondent becomes more concerned about his anonymity, then the mean square error may be larger. A field study of limited scope conducted in Taichung, Taiwan indicated that this multiple trial RRT model is at least as feasible as, if not more feasible than, the conventional single trial RRT. There was no sign suggesting cooperation of respondents had deteriorated because each was asked to repeat the procedures three times. If the number of trials did not exceed three, we believe that the increase in the cost of survey and "exhaustion" of respondents from repeated administration of the same set of questions would be negligible. Hence, we believe that this multiple trial technique is a feasible and useful survey method for study of various contemporary social problems of sensitive nature. More field testing, particularly in different socio-cultural settings, is necessary however, before a general conclusion may be drawn.