Optional Randomized Response Technique Research Articles

Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

Randomized Response (RR) Technique (RRT) pioneered by Warner (1965) is a useful tool to elicit responses on sensitive characteristics, such as induced abortions, drug abuse, drunken driving, total amount of counterfeit notes of a particular denomination held by individuals in the population, etc. There exists a huge literature on Randomized Response (RR) devices for estimation of finite population mean of quantitative variables, sensitive in nature mostly based on Eichhorn and Hayre (1983). Device-I and Device-II vide Chaudhuri and Christofides (2013) allow estimation of population mean of sensitive quantitative variables using sample chosen by a general sampling design. On the other hand, Item Count Technique (ICT), described elaborately in Chaudhuri and Christofides (2013), is an alternative to RRT for respondents who do not choose to provide RRs. While some respondents may find a variable as sensitive, others may find it innocuous enough to provide a direct response (DR) about his/her true value. In such a case, Optional Randomized Response (ORR) Technique (ORRT) with options for DR and RR was introduced by Chaudhuri and Mukherjee (1985). Pal (2007) proposed an ORR device which offers choices for RR and ICT to the respondents for giving their answers. A new ORRT with options for DR, RR and ICT was provided by Shaw and Pal (2021) for eliciting indirect responses on sensitive characteristics. As this device relates to estimation of population proportion of sensitive characteristics, an attempt has been made to extend it for sensitive quantitative variables. Further, to take care of individuals’ varying choices for DR, RR and ICT and to protect the privacy of the respondents’ choices, this paper develops an ORR device allowing the respondents chosen by a general sampling design, to choose any one of the three options according to their choices. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 155-170

Applying ORRT for the estimation of population variance of sensitive variable

The current work is driven to provide a collaborated variance estimator for the estimation of population variance by employing optional randomized response technique (ORRT) in order to boost variance estimation. The formulations of bias and mean squared error of the recommended variance estimator under ORRT are established to the first degree of approximation. To assess the performance of the suggested estimator by utilizing a unified measure and efficiency of the estimator, a simulation study is conducted by using R software. According to the findings and graphical representations, it is observed that our proposed estimator is much more convenient than competing estimator(s).

An Improved Class of Estimators Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique

In this paper we have suggested a class of estimators of population mean of sensitive variable under optional randomized response technique as reported in Gupta et al  (2014). We have obtained the mean squared error (MSE) of the suggested class of estimators up to the first order of approximation. The optimum conditions are obtained at which the (MSE) of the proposed class of estimators is minimum. An empirical study is carried out to show the performance of the suggested class of estimators over existing estimators .It is found that the performance of proposed class of estimators is better than the existing estimators including Grover and Kaur (2019).

Mean Estimation of A Sensitive Variable Using Optional Randomized Response Technique in Two-Phase Sampling When Non-response and Measurement Error are Simultaneously Present

Mean Estimation of A Sensitive Variable Using Optional Randomized Response Technique in Two-Phase Sampling When Non-response and Measurement Error are Simultaneously Present

An efficient application of scrambled response approach to estimate the population mean of the sensitive variables

In the presence of one auxiliary variable and two auxiliary variables, we analyze various exponential estimators. The ranks of the auxiliary variables are also connected with the study variables, and there is a linkage between the study variables and the auxiliary variables. These ranks can be used to improve an estimator's accuracy. The Optional Randomized Response Technique (ORRT) and the Quantitative Randomized Response Technique are two techniques we utilize to estimate the sensitive variables from the population mean (QRRT). We used the scrambled response technique and checked the proposed estimators up to the first-order of approximation. The mean square error (MSE) equations are obtained for all the proposed ratio exponential estimators and show that our proposed exponential type estimator is more efficient than ratio estimators. The expression of mean square error is obtained up to the first degree of approximation. The empirical and theoretical comparison of the proposed estimators with existing estimators is also be carried out. We have shown that the proposed optional randomized response technique and quantitative randomized response model are always better than existing estimators. The simulation study is also carried out to determine the performance of the estimators. Few real-life data sets are also be applied in support of proposed estimators. It is observed that our suggested estimator is more efficient as compared to an existing estimator.

The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models

This paper addresses three important issues of survey sampling: social desirability bias, measurement error and non-response simultaneously. We suggested a combined family of regression-cum-exponential estimators for estimating the population mean of sensitive variable in the presence of measurement error and non-response simultaneously using optional randomized response technique models. The properties of the suggested estimator(s) have been studied and efficiency conditions have been derived. A simulation study is carried out to support the theoretical findings and shows significant improvement in terms of percent relative efficiency (PRE).

Partial optional randomized response technique with calibration weighting to adjust non-response in successive sampling

Partial optional randomized response technique with calibration weighting to adjust non-response in successive sampling

How privacy may be protected in optional randomized response surveys

Abstract There are materials in literature about how privacy on stigmatizing features like alcoholism, history of tax-evasion, or testing positive in AIDS-related testing may be partially protected by a proper application of randomized response techniques (RRT). The paper demonstrates what amendments are necessary for this approach while applying optional RRTs covering qualitative characteristics, permitting a sampled respondent either to directly reveal sensitive data or choose a randomized response respectively with complementary probabilities. Only a few standard RRTs are illustrated in the text.

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.

An Improved Two-stage Stratified Randomized Response Model for Estimating Sensitive Proportion

This article is about making correction in Tarray, Singh, and Zaizai model and further improving it when stratified random sampling is necessary. This is done by using optional randomized response technique in stratified sampling using a combination of Mangat and Singh, Mangat, and Greenberg et al. models. The suggested model has been studied assuming proportional and Neyman allocation schemes. Numerical results show larger gains in efficiency. Through a detailed numerical study, it is established that the suggested model is relatively more efficient than the Kim and Warde model and the models mentioned above.

An Improved Exponential Type Estimator Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique

In this paper, we improve the efficiency of Koyuncu et al (2014)’s estimator of population mean of sensitive variable by replacing Traditional Randomized response technique with Optional Randomized response technique as suggested by Gupta et al (2014). The mean square error of proposed estimator is obtained, up to first order of approximation, and is compared with mean square error of various existing estimators theoretically as well as numerically.

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.

Optional randomized response techniques for quantitative characteristics

Gupta et al. and Huang considered optional randomized response techniques where the probability of choosing the randomized (or direct) response is fixed for all the respondents. In this paper the assumption of the constant probability of choosing the option has been relaxed by dividing respondents into two groups: one group provides direct response and the second a randomized response. The method of estimation of the population mean and variances under the modified assumption are obtained. Relative efficiencies of the proposed techniques are compared theoretically and empirically.

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.

Optional randomized response technique in two-phase sampling

ABSTRACTTwo-phase optional randomized response (TORR) technique has been proposed. The proposed randomized response (RR) performs much better in general than the existing RR techniques. Theoretical and numerical illustrations identified conditions of superiority of the proposed TORR over the existing comparable optional randomized response (ORR) techniques.

A Dexterous Optional Randomized Response Model

This article addresses the problem of estimating the proportion π S of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is more efficient than Kim and Warde stratified randomized response model and Mangat model.

A regression estimator for finite population mean of a sensitive variable using an optional randomized response model

ABSTRACTKalucha et al. (Kalucha G., Gupta S., Dass B. K. (accepted). Ratio estimation of finite population mean using optional randomized response models. Journal of Statistical Theory and Practice) introduced an additive ratio estimator for finite population mean of a sensitive variable in simple random sampling without replacement and showed that this estimator performs better than the ordinary mean estimator based on an optional randomized response technique (RRT). In this paper, we introduce a regression estimator that performs better than the ratio estimator even for the modest correlation between the study and the auxiliary variables. A comparison of the proposed estimator with the corresponding ratio estimator and the ordinary RRT mean estimator is carried out theoretically, and is also illustrated with a simulation study.

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Auxiliary information is commonly used in sample surveys in order to achieve higher precision in the estimates. In this article we are concerned with the utilization of auxiliary information in the estimation stage in simple random sampling without replacement (SRSWOR), making use of an optional randomized response model proposed by Gupta et al. (2010). The underlying assumption is that the primary variable is sensitive in nature but a nonsensitive auxiliary variable exists that is positively correlated with the primary variable. We propose a ratio estimator of finite population mean and call it the additive ratio estimator. Expressions for the bias and mean square error of the proposed estimator are obtained to first order of approximation. Efficiency comparisons with the ordinary optional randomized response technique (RRT) mean estimator of Gupta et al. (2010) are carried out both theoretically and numerically. A simulation study is presented to evaluate the performance of the proposed estimator.

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).

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.