Optional Randomized Response Research Articles

Mean and sensitivity estimation using optional scrambled randomized response technique

In this paper, a new optional randomized response model has been proposed for estimating the population mean of a sensitive variable and sensitivity level in presence of scrambled response under simple random sampling. The properties of proposed model are described and verified its theoretical results with empirical analysis. Both efficiency and privacy measures are also explained and it is found that the proposed optional scrambled randomized response model outperform as compared to some existing additive and multiplicative models.

Estimation of finite population mean of a sensitive variable using three-stage optional RRT in the presence of non-response and measurement errors

The purpose of this study is to present a generalized class of estimators using the three-stage optional randomized response technique (RRT) in the presence of non-response and measurement errors on a sensitive study variable. The proposed estimator makes use of dual auxiliary information. The expression for the bias and mean square error of the proposed estimator are derived using Taylor series expansion. The proposed estimator's applicability is proven using real data sets. A numerical study is used to compare efficiency of the proposed estimator with adapted estimators of the finite population mean. The suggested estimator performs better than adapted ordinary, ratio, and exponential ratio-type estimators in the presence of both non-response and measurement errors. The efficiency of the proposed estimator of population mean declines as the inverse sampling rate, non-response rate, and sensitivity level of the survey question increase.

A versatile optional randomized response technique for use with sensitive surveys

In data collection from human participants, researchers in almost every survey get refusals and/or false responses from the respondents. Such refusals and false reporting are particularly common in sample surveys where the participants are asked to answer questions on sensitive topics such as cheating in examination, illegal income, marks obtained in last examination, students’ satisfaction from the teaching method, and amount of money spent on luxury items, etc. A popular approach to deal with the problem of refusals and untruthful responses is the randomized response technique. This paper introduces a randomized response model which is more precise than the available models. The proposed randomized scrambling procedure guarantees the privacy protection of the respondents for motivating them to participate in the survey.

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).

Introducing an efficient alternative technique to optional quantitative randomized response models

In social surveys on sensitive characteristics, optional randomized response models give the respondents the option to either report the true response or report the scrambled response. If any respondent finds that the question being asked does not feel sensitive, he/she reports the true response. In the existing variants of optional randomized response models, the researcher doesn’t know whether the respondent opted for the correct response or for a scrambled response. In practice, some of the respondents may have no problem in disclosing to the researcher that they are giving the true response and hence not opting for scrambling. This paper presents an alternative procedure to optional scrambling randomized response models, where each respondent has the choice whether or not to disclose to the researcher that he/she is giving the true response. Alternative modified versions of three existing scrambling randomized response models are presented. It is found that the efficiency of the quantitative randomized response models improves if the exact number of respondents who are opting for scrambling, is known to the researcher. Besides improvement in efficiency, the level of the respondent-privacy is the same as that of the existing models, thus resulting in an improvement in the overall quality of the existing models.

Additive ratio type exponential estimator of finite population mean of sensitive variable using non-sensitive auxiliary information based on optional randomized response model

The appropriate use of auxiliary information in sample surveys increases the efficiency of estimator for parameter of interest. In this paper, we have proposed an exponential type estimator for the population mean of a sensitive study variable based on an optional randomized response model by using the known information on a non-sensitive auxiliary variable. Expressions for the bias and the mean square error (MSE) of the proposed estimator are derived, up to first order of approximation. For this proposed estimator, efficiency comparisons with the existing estimators have been carried out both theoretically and numerically. It has been shown that our proposed estimator perform better than the existing estimators based on the same optional randomized response model even for the small correlation between auxiliary variable and study variable. To support the results obtained, we have also studied the performance of the proposed exponential estimator using simulation technique.

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

An alternative approach for construction of strata using quantified sensitivity level

The study is investigated on an alternative method for the construction of strata using sensitivity level when the samples are selected with simple random sampling with replacement (SRSWR) and the data are collected by scrambled optional randomization technique on the sensitive characters. Thus, the optional randomized response model , where k is a random variable having value 1 if the response is scrambled and 0 otherwise, was considered for finding out Approximate Optimum Strata Boundaries by minimizing the variance of the estimator . The cum. was proposed for finding out Approximate Optimum Strata Boundary in Neyman allocation for the optional scrambled response. This is applicable for wider classes of sampling design and estimators in stratification. The proposed rule on optional scrambled randomized response is efficient and can be used effectively for the construction of optimum strata boundary via Rectangular, Right triangular and Exponential distribution.

A generalized class of exponential type estimators for estimating the mean of the sensitive variable when using optional randomized response model

In this article, we propose a generalized class of exponential type estimators for estimating the mean of delicate variable in the existence of non-sensitive two auxiliary variables. The performance of mean estimator is obtained by using generalized two stage optional randomized response model. The expression for the bias and the mean square error are obtained up to first degree of approximation. Certain special cases for the generalized class are discussed. An extensive simulation study is performed to determine the performance of the estimators. It is observed that the suggested class of estimators performs more efficiently than some existing estimators.

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.

Generalized exponential type estimator for the mean of sensitive variable in the presence of non-sensitive auxiliary variable

We proposed a generalized two stage optional randomized response model by single sample approach and developed a generalized exponential type estimator for the mean of sensitive variable using information from a non-sensitive auxiliary variable. Privacy protection and some special cases for the suggested model has also been discussed. Simulation and numerical study are carried out to assess the performance of the suggested estimator. We compare the proposed model with some existing estimators and conclude that our proposed model is more efficient under certain conditions.

Improved Randomized Response in Optional Scrambling Models

In the present study, we discuss the issue of increasing the respondents cooperation in sensitive surveys. When the question is highly sensitive then the cooperation from the respondents is decreased. We propose two optional randomized response models (ORRMs) to increase the respondents cooperation. A comparison of proposed ORRMs with [1] two- and three-stage models have been made. It is found that, in estimating mean and sensitivity level, the proposed strategies perform better than [1] two-and three-stage models.A comparison is also made among the [1] two- and three-stage models and proposed ORRMs to identify the best one. Numerical illustration are also given in favor of the algebraic results.

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.

A Remark on Gupta, Gupta and Singh Optional Randomized Response Model

Abstract Gupta et al (2002) suggested an optional randomized response model under the assumption that the mean of the scrambling variable S is ‘unity’ [i.e. µs = 1]. This assumption limits the use of Gupta et al’s (2002) randomized response model. Keeping this in view we have suggested a modified optional randomized response model which can be used in practice without any supposition and restriction over the mean (µs ) of the scrambling variables S. It has been shown that the estimator of the mean of the stigmatized variable based on the proposed optional randomized response sampling is more efficient than the Eicchorn and Hayre (1983) procedure and Gupta et al’s (2002) optional randomized technique when the mean of the scrambling S is larger than unity [i.e. µs > 1]. A numerical illustration is given in support of the present study.

Improved Estimation of Sensitive Mean Using Hybrid of Partial and Optional Scrambling in the Presence of Non-Sensitive Auxiliary Information

This article is about studying ratio, product and regression methods for estimating sensitive mean using a two-stage optional randomized response model by Gupta et al. (2010) and information on non-sensitive auxiliary variable. In particular, the additive randomized response model is used to further enhance the efficiency of the ratio, product and regression estimators (Gupta et al., 2010). We compare our proposed auxiliary information based two-stage optional randomized response estimator with recently proposed auxiliary information-based estimators. Through algebraic comparisons, it is shown that the proposed ratio, product and regression estimators are better than the corresponding estimators proposed in some recent studies. The results are also supported by a numerical study.

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.