Randomized Response Technique Research Articles

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.

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.

Respondent-specific randomized response technique to estimate sensitive proportion

In estimating the proportion of people bearing a stigmatizing characteristic in a community of people, randomized response techniques are plentifully available in the literature. They are implemented essentially using boxes of similar cards of two distinguishable types. In this paper, we propose a more general procedure using five different types of cards. A respondent-specific randomized response technique is also proposed, in which respondents are allowed to build up the boxes according to their own choices. An immediate objective for this change is to enhance, sense of protection of privacy of the respondents. But as by-products, higher efficiency in terms of actual coverage percentages of confidence intervals and related features are demonstrated by a simulation study, and superior jeopardy levels against divulgence of personal secrecy are also reported to be achievable. AMS subject classification: 62D05

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).

How to use randomized response survey data at hand by a specific procedure to judge its efficiency versus a possible rival

It is well-known that given survey data at hand by a given method, it is possible to examine how this method promises to fare vis- à -vis another one that might have been employed but not actually implemented. We illustrate how this may be extended to cover Randomized Response (RR) Techniques (RRT) by citing a few RR procedures in combination with a few sample selection methods generally in use. Developing the theory, simulated results are presented to demonstrate interesting numerical findings in this context.

Estimation of Hidden Logits Using Several Randomized Response Techniques

In survey sampling, we aspire to obtain sound and consistent responses, which are not achieved while dealing with sensitive issues. Frequently, respondents give elusive responses to sensitive questions, so we employ randomized response techniques that facilitate finding an appropriate proportion of socially sensitive characteristics. In the present study, we proposed a hidden logit estimation method using Huang, Warner, and Mangat’s randomized response techniques. This study depicts that the estimates become closer to the standard logits as the values of p increase. We found that the hidden logit estimates obtained by the Huang randomized response technique were nearer to the parametric values, in contrast to the other existing techniques, and we demonstrate an increase in accuracy as well. The simulation-based AIC and SIC values are used to assess model performance. We found that the Huang model is the best model for the proposed hidden logit method. This paper contributes towards the application of logistic models in the case of sensitive or socially stigmatized issues.

Synthesized randomized response techniques

Reducing response bias in survey research is important in ensuring that the data collected accurately represents the population of interest. This study proposes the synthesized random response technique (SRRT) estimator as an efficient method to reduce response bias in this regard. We compared the proposed SRRT estimator with other conventional techniques, such as the Hybrid Tripartite Randomized Response Technique (HTRRT), the Alternative Tripartite Randomized Response Technique (ATRRT), and the Two-Stage Unrelated Question Randomized Response Model for Estimating Prevalence of Stigmatized Attributes (TSUQRRMEPSA). Our results show that the proposed SRRT estimator consistently produces more efficient estimates than other conventional techniques as sample sizes increase. As a result, the proposed SRRT estimator have the potential to enhance the accuracy of survey data, which is sensitive for informed decision-making. Hence, the proposed method is more efficient in reducing response bias than other conventional methods.