Randomized Response Technique Research Articles

An improved variant of quantitative randomized response techniques using forced responses

The randomized response technique has gained a wide popularity among survey researchers over the past few decades. Randomized response procedure is applicable in a variety of fields including sociology, psychology, business, and education, etc. It is a useful method which helps the researcher in dealing with the high non-response rates in sample surveys on sensitive issues such as monthly income, traffic rules violations, income tax amount, and expenditure on luxury items, etc. We introduce an optimal scrambling technique which uses forced responses. The algebraic properties of the estimator of population mean using the suggested technique have been derived. For the purpose of comparison with existing models, the different measures of model-evaluation have been obtained. Our analysis suggests that the new quantitative technique using forced responses is better than the available scrambling techniques not only in efficiency, but also in the combined metric of model’s efficiency and level of privacy, which make it more useful than the available models for practical problems. Using real-world example, we illustrate its practical implementation to sensitive sample surveys.

A class of infinite number of unbiased estimators using weighted squared distance for two-deck randomized response model

ABSTRACT We develop a collection of unbiased estimators for the proportion of a population bearing a sensitive characteristic using a randomized response technique with two decks of cards for any choice of weights. The efficiency of the estimator depends on the weights, and we demonstrate how to find an optimal choice. The coefficients of skewness and kurtosis are introduced. We support our findings with a simulation study that models a real survey dataset. We suggest that a careful choice of such weights can also lead to all estimates of proportion lying between [0, 1]. In addition, we illustrate the use of the estimators in a recent study that estimates the proportion of students, 18 years and over, who had returned to the campus and tested positive for COVID-19.

Estimation of sensitive trait proportion using Kuk’s randomized response model with auxiliary information

Different strategies have been developed in survey sampling to address the issue of missing observations and non response. Asking direct questions can be difficult in getting a real response. To get over this problem, we can utilize an indirect approach, such as the randomized response technique (RRT) which is frequently used to estimate the proportion of sensitive trait. In this work, when population level data on a non-sensitive auxiliary variable is available, we provide an enhanced class of estimators for sensitive traits. This class of estimators is based on a generalization of the well-known Kuk’s estimator and a usual difference estimator proposed by Diana and Perri (2009). We verify the findings with survey information obtained from the University of Wah in Pakistan and a data set previously utilized by Zaizai (2006).

Tri-Phase Implementation of an Innovative Fuzzy Logic Approach for Decision-Making

This paper proposes a novel approach to decision-making based on a three-phase application of a new fuzzy logic model that embraces the principles of symmetry by balancing competing objectives in data collection and analysis. Our study, which employs a three-stage stratified random sample strategy with a randomized response technique, addresses the critical challenges of cost management and volatility reduction. Using the alpha-cut method, our model creates an effective allocation strategy that finds a balance between cost constraints and variance reduction objectives. We use numerical examples from real-world scenarios to demonstrate our approach’s durability and practicality. Our revolutionary technique maintains data quality and cost-effectiveness while offering a game-changing answer to sensitive information acquisition concerns. By combining randomized response techniques and fuzzy logic, this study establishes a new standard for decision-making models that prioritizes both data-gathering precision and privacy preservation, encapsulating the essential principle of symmetry in balancing competing aims.

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.

An Optimised Optional Randomised Response Technique

SummaryIn this paper, we begin by reviewing the optional randomised response technique estimator (ORRTE) developed by Chaudhuri and Mukerjee for estimating the proportion of a sensitive characteristic in a population. We show that their estimator is unbiased and has smaller variance than the Warner's estimator. Then we make an attempt at developing an optimised optional randomised response technique estimator (OORRTE). The proposed OORRTE is shown to be more efficient than the ORRTE. Findings from simulation studies are discussed and interpreted for various situations. Sample sizes for the Warner's estimator, the ORRTE and the OORRTE are computed based on power analysis introduced by Ulrich, Schroter, Striegel and Simon. Finally, we include an application to real data on COVID‐19 by considering it to be partially sensitive variable; that is, sensitive to some but not to others. The data used are included in the paper and the R‐codes used in the simulation study are documented in online material.

A novel randomized scrambling technique for mean estimation of a finite population

In recent decades, the randomized response technique has attracted researchers due to its usefulness in sensitive surveys. The randomized response procedure is used for the collection of responses on sensitive issues such as cheating in examination, income earned through illegal sources, expenditure on luxury items, and amount of tax paid, etc. This study introduces a new variant of quantitative randomized response models for use with sample surveys where the variable of interest is quantitative. The properties of a mean estimator based on the new technique have been studied. Further, the combined and separate evaluation metrics for efficiency and privacy level have also been derived and compared with those of the existing methods. Further, a simulation study has been conducted to prove the improvement in the degree of privacy protection and efficiency. The findings reveal that the suggested randomized response technique is not only more efficient than the existing techniques, but also improves the joint measure of efficiency and respondents’ privacy, making it preferable over the existing techniques. A real-world example of a sample survey through the suggested model is also presented which illustrates its usefulness in practical surveys on sensitive issues.

Randomized response technique in agricultural surveys

Randomized response technique in agricultural surveys

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

Accounting for Measurement Error and Untruthfulness in Binary RRT Models

This study examines the effect of measurement error on binary Randomized Response Technique models. We discuss a method for estimating and accounting for measurement error and untruthfulness in two basic models and one comprehensive model. Both theoretical and empirical results show that not accounting for measurement error leads to inaccurate estimates. We introduce estimators that account for the effect of measurement error. Furthermore, we introduce a new measure of model privacy using an odds ratio statistic, which offers better interpretability than traditional methods.

Aiding the well celebrated Kuk's randomized response technique through auxiliary and prior information

Asking direct questions in face to face surveys about sensitive traits is an intricate issue. One of the solutions to this issue is the randomized response technique (RRT). Being the most widely used indirect questioning technique to obtain truthful data on sensitive traits in survey sampling RRT has been applied in a variety of fields including behavioral science, socio-economic, psychological, epidemiology, biomedical, criminology, data masking, public health engineering, conservation studies, ecological studies and many others. This paper aims at exploring the methods to subsidize the randomized response technique through additional information relevant to the parameter of interest. Specifically, we plan to contribute by proposing more efficient hybrid estimators compared to existing estimator based on (Kuk, 1990) [31] family of randomized response models. The proposed estimators are based on the methodology of incorporating the pertinent information, available on the basis of either historical records or expert opinion. Specifically, in case of availability of auxiliary information, the regression-cum-ratio estimator is found to be the best to further enhance the estimation through (Kuk, 1990) [31] model while the (Thompson, 1968) [49] shrinkage estimation is observed to be yielding more precise and accurate estimator of sensitive proportion. The findings in this study signify the importance of the proposed methodology. Additionally, to support the mathematical findings, a detailed numerical investigation to evaluate the comparative performances is also conducted. Based on performance analysis, overwhelming evidences are witnessed in the favor of proposed strategies.

An efficient estimator of population variance of a sensitive variable with a new randomized response technique

In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.

Binary Randomized Response Technique (RRT) models under measurement error

In real-world surveys, measurement error is usually inevitable. It is the difference between the actual value of the variable being measured and its recorded value. Many authors in the field of Randomized Response Technique (RRT) have studied the impact of measurement error on quantitative RRT models, but there are no such studies for binary RRT models. In this article, we propose a binary RRT model under measurement error based on the previous work of Warner (1965). A simulation study is presented to validate the theoretical findings. Simulations show that the measurement error factor cannot be ignored when using binary RRT models, and the proposed estimator from the binary RRT model under measurement error performs well.

A Hybrid Paillier Encryption and Randomized Response Technique Model for Surveying Sensitive Questions with Binary Response

A Hybrid Paillier Encryption and Randomized Response Technique Model for Surveying Sensitive Questions with Binary Response

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.

Multicriteria Evaluation of Randomized Response Techniques for Population Mean

Increasing demand in surveys focused on quantitative characteristics (population mean among others) of controversial issues like corruption, tax evasion, drugs consumption of sensitive variables like spending on drugs or illegal sources of income which lead to lively research, are of randomized response techniques for quantitative variables. Therefore, we propose complex multicriteria evaluation methodology for randomized response techniques for population mean. Based on extensive review in the literature, following ranges of criteria were proposed: statistical properties of estimator, implementation and parameter choice, respondent burden and credibility and confidentiality protection of respondents’ data. Finally, we evaluate in this setting standard techniques using scramble variables and recently proposed techniques of dichotomous question.

Response Aggregation to Obtain Truthful Answers to Sensitive Questions: Estimating the Prevalence of Illegal Purchases of Prescription Drugs

This research proposes a simple, new technique to obtain truthful answers to sensitive, categorical questions. The paired response technique (PRT) asks participants to merely report the sum of the answers to two paired questions, one baseline and one sensitive, with the answers to each question known only to the participants. The technique then statistically infers the prevalence of the sensitive characteristic and its potential drivers from the association of the baseline question with other questions in the survey. Monte Carlo simulations demonstrate the performance of the PRT under varying conditions. A representative survey (n = 4,649) in the Netherlands about legal and illegal purchases of prescription drugs to enhance sexual performance reveals that 17.4% of the target population has purchased medication to enhance sexual performance at least once. In contrast, in a control group surveyed with direct questioning, only 5.1% admit having done so. The great majority of these individuals opt to purchase illegally. Two further empirical applications, respectively, in the United States and the United Kingdom, show that the PRT reduces cognitive and affective costs of survey participation compared with a state-of-the-art randomized response technique for categorical questions.

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).

A comparative study of randomized response techniques using separate and combined metrics of efficiency and privacy.

In social surveys, the randomized response technique can be considered a popular method for collecting reliable information on sensitive variables. Over the past few decades, it has been a common practice that survey researchers develop new randomized response techniques and show their improvement over previous models. In majority of the available research studies, the authors tend to report only those findings which are favorable to their proposed models. They often tend to hide the situations where their proposed randomized response models perform worse than the already available models. This approach results in biased comparisons between models which may influence the decision of practitioners about the choice of a randomized response technique for real-life problems. We conduct a neutral comparative study of four available quantitative randomized response techniques using separate and combined metrics of respondents' privacy level and model's efficiency. Our findings show that, depending on the particular situation at hand, some models may be better than the other models for a particular choice of values of parameters and constants. However, they become less efficient when a different set of parameter values are considered. The mathematical conditions for efficiency of different models have also been obtained.