Optional Randomized Response Research Articles

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.

Improved randomized response models in additive scrambling

In this investigation, we consider the problem of procuring the reliable information on stigmatizing variable. Two optional randomized response models are proposed for efficient estimation of mean and sensitivity level. A comparison of proposed optional randomized response models (ORRMs) with Huang (2010) and Gupta et al. (2010) models have been made. It is found that the proposed strategies perform better than those of Huang (2010) and Gupta et al. (2010) models whether it is estimation of mean or sensitivity level. A comparison is also made among the Huang (2010), Gupta et al. (2010) and proposed ORRMs to identify the best one. Percentage relative efficiency comparisons are also made to study the performance of the proposed procedures.

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.

A two-step approach to ratio and regression estimation ofnite population mean using optional randomized response models

A two-step approach to ratio and regression estimation ofnite population mean using optional randomized response models

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 STRATIFIED MANGAT AND SINGH'S OPTIONAL RANDOMIZED RESPONSE MODEL USING PROPORTIONAL AND OPTIMAL ALLOCATION

This paper suggests a stratified optional randomized response model based on Mangat and Singh (1994) model that has proportional and optimal allocation and larger gain in efficiency. Numerically it is found that the suggested model is more efficient than Kim and Warde (2004) stratified randomized response model and Mangat and Singh (1994) model. Graphical representations are also given in support of the present study.

Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010)? We will note that the answer to the first question is “yes” but the answer to the second question is “no.”

A Three-Stage Optional Randomized Response Model

In Gupta et al. (2010; 2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a “three-stage optional randomized response model,” a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresp...

Some Optimality Issues in Estimating Two-Stage Optional Randomized Response Models

SYNOPTIC ABSTRACTGupta, Gupta and Singh (2002) introduced an optional randomized response (ORR) model for estimating the mean and the sensitivity level of a sensitive variable. In an ORR model the respondent is asked to provide a scrambled response only if the respondent considers the question sensitive and a truthful response otherwise. The researcher does not know which type of response is provided. The idea is that a question that is sensitive for one person may not be sensitive for another person. Gupta, Shabbir and Sehra (2010) extended this model to a two-stage ORR model where in the first stage a randomly selected proportion (T) of the respondents is asked to provide a truthful response. The rest of the respondents are asked to go to Stage-2 where they respond according to the ORR model. The main focus of this paper is on finding an optimal value of T for which the two-stage model performs better than the corresponding one-stage model.

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.

An optional scrambled randomized response technique for practical surveys

Eichhorn and Hayre (J Stat Plan Inference 7:307–316, 1983) introduced the scrambled response technique to gather information on sensitive quantitative variables. Singh and Joarder (Metron 15:151–157, 1997), Gupta et al. (J Stat Plan Inference 100:239–247, 2002) and Bar-Lev et al. (Metrika 60:255–260, 2004) permitted the respondents either to report their true values on the sensitive quantitative variable or the scrambled response and developed the optional randomized response (ORR) technique based on simple random sample with replacement (SRSWR). While developing the ORR procedure, these authors made the assumption that the probability of disclosing the true response or the randomized response (RR) is the same for all the individuals in a population. This is not a very realistic assumption as in practical survey situations the probability of reporting the true value or the RR generally varies from unit to unit. Moreover, if one generalizes the ORR method as developed by these authors relaxing the ‘constant probability’ assumption, the variance of an unbiased estimator for the population total or mean can not be estimated as this involves the unknown parameter, ‘the probability of revealing the true response’. Here we propose a modified ORR procedure for stratified unequal probability sampling after relaxing the assumption of ‘constant probability’ of providing the true response. It is also demonstrated with a numerical exercise that our procedure produces better estimator for a population total than that provided by the method suggested by the earlier authors.

Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling

This paper considers the problem of procuring reliable information on sensitive quantitative characteristics without exposing respondents’ identities. A generalized optional randomized response procedure is proposed, which enables us to estimate some unknown population parameters unbiasedly. In particular, conditions for the assurance of unbiased estimations of mean, variance and sensitivity level are studied. Efficiency comparisons are also carried out to study the performance of the proposed procedure.

Optional randomized response in stratified unequal probability sampling—A simulation based numerical study with Kuk’s method

Warner’s pioneering randomized response (RR) device, as a method for reducing evasive answer bias while estimating the proportion of people in a community bearing a sensitive attribute, has been studied extensively over the last four decades. In many practical surveys it was observed that a character considered to be stigmatizing by a group of respondents did not appear to be such to another group, and direct responses (DR’s) to divulge its true characteristics were offered. Chaudhuri and Mukerjee (Calcutta Stat Assoc Bull 34:225–229, 1985; Randomized response: theory and techniques. Dekker, New York, 1988) introduced the concept of optional RR (ORR) to accommodate direct responses offered by such respondents. Since unequal probability stratified sampling is followed in large-scale socio-economic surveys, it is necessary to develop RR procedures for such complex surveys. Kuk’s method is extended to varying probability stratified sampling when RR’s as well as DR’s are permitted. A numerical study comparing the performance of alternative procedures is also reported.

Estimation for sensitive characteristics using optional randomized response technique

This paper considers the problem of procuring honest responses to estimate the population mean of sensitive quantitative characteristics. It aims at pointing out that potential difference between sub-populations seems to be unnoticed under the usual optional randomized response technique. To make an extension to cover all the situations, we propose two alternative survey procedures that enable us to estimate the mean and the variance unbiasedly. Estimation for the sensitivity level of a question is under consideration as well. Efficiency comparisons have also been carried out to study the performances of the proposed procedures.

Improvement upon Warner's model with an optional randomized response technique

Improvement upon Warner's model with an optional randomized response technique

Optional Randomized Response Techniques for Complex Survey Designs

AbstractGupta, Gupta and Singh (2002) proposed an optional randomized response (ORR) technique based on SRSWR sampling using an unrealistic assumption that the probability of providing the true/randomized response for all the individuals in a population is the same. In this paper an alternative ORR has been proposed for an arbitrary sampling design. Expressions for the estimators of the population mean, variance and unbiased estimator for the variance have been provided. It is shown that the estimator, based on an ORR, is more efficient than an estimator derived from a non‐ORR technique. Sufficient conditions for the superiority of the proposed estimator over the existing estimator provided by Gupta et al.'s (2002) have also been established. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Estimation of sensitivity level of personal interview survey questions

In this paper, an optional randomized response model is proposed. The estimator of the mean of the stigmatized variable based on the optional randomized response sampling is shown to be more efficient than the usual estimator of the mean based on randomized response technique method. In addition to estimating population mean and variance, it has been shown that the optional randomized response technique is useful in quantifying the sensitivity levels of the questions in the personal interview surveys. An estimator for the sensitivity level of a question is proposed and an empirical study is carried out to show the validity of the proposed estimation technique. We also propose a test for the sensitivity level of the stigmatized variable.