Randomized Response Procedure Research Articles

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.

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.

A criterion for privacy protection in data collection and its attainment via randomized response procedures

Randomized response (RR) methods have long been suggested for protecting respondents’ privacy in statistical surveys. However, how to set and achieve privacy protection goals have received little attention. We give a full development and analysis of the view that a privacy mechanism should ensure that no intruder would gain much new information about any respondent from his response. Formally, we say that a privacy breach occurs when an intruder’s prior and posterior probabilities about a property of a respondent, denoted $p$ and $p_{*}$, respectively, satisfy $p_{*} h_{u}(p)$, where $h_{l}$ and $h_{u}$ are two given functions. An RR procedure protects privacy if it does not permit any privacy breach. We explore effects of $(h_{l},h_{u})$ on the resultant privacy demand, and prove that it is precisely attainable only for certain $(h_{l},h_{u})$. This result is used to define a canonical strict privacy protection criterion, and give practical guidance on the choice of $(h_{l},h_{u})$. Then, we characterize all privacy satisfying RR procedures and compare their effects on data utility using sufficiency of experiments and identify the class of all admissible procedures. Finally, we establish an optimality property of a commonly used RR method.

Variance estimation of persons infected with AIDS under ranked set sampling

This paper deals with the analysis of the estimation of the variance of a sensitive variable. The randomized response (RR) procedure gives confidence to the interviewee that his/her information on private (sensitive variable) is protected. In general, a simple random sampling (SRS) with replacement design is used for selecting a sample. We develop a model for the estimation of the variance of sensitive variable in randomized response procedure, when ranked set sampling (RSS) design is used under ranking criteria. The usual gain in accuracy related to the use of ranked set sampling is revealed. The performance of the proposed model is demonstrated using data provided by a study of samples of persons infected with AIDS disease.

New Randomized Response Procedure for Finding Optimal Solution Using Branch and Bound Method

New Randomized Response Procedure for Finding Optimal Solution Using Branch and Bound Method

Improved randomized response in additive scrambling models

ABSTRACTRandomized response models deal with stigmatizing variables appearing in health surveys. Additive and subtractive scrambling in split sample and double response yield unbiased mean and sensitivity estimators of high precision. The split sample method is protective of privacy. The double response method is as protective only conditionally. To achieve the maximum efficiency, the scrambling variables must be similar to each other and the probability of obtaining a true response must be as large as possible. The randomized response procedures yield more efficient estimates of the average total number of classes missed by university students.

Randomized Response Procedure for the Estimation of the Population Ratio using Ranked Set Sampling

In this study we deal with the estimation of the population ratio, when a Randomized Response (RR) procedure is used for collecting responses and Ranked Set Sampling (RSS) is the selection method. The variances of the suggested estimators are calculated. Comparisons between different estimators are presented.

Efficient use of a two-stage randomized response procedure

Towards the search for improving the randomized response models used to estimate a population proportion bearing a sensitive characteristic, a new model, based on the use of a two-stage randomized response procedure, is proposed. The condition under which the proposed estimator is more efficient than the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator has been obtained. An empirical study has also been performed to examine the relative efficiency of the proposed estimator with respect to the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator. Moreover, the proposed estimator can be easily adjusted to be more efficient than the Warner [J. Amer. Statist. Assoc. 60 (1965) 63–69], Mangat and Singh [Biometrika 77 (1990) 439–442], Mangat [J. R. Stat. Soc. Ser. B Stat. Methodol. 56 (1994) 93–95] and Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimators.

A randomized response procedure for multiple-sensitive questions

The Randomized Response (RR) technique is a well-established interview procedure which guarantees privacy protection in social surveys dealing with sensitive items. The RR method assumes a stochastic mechanism to create uncertainty about the true status of the respondents in order to ensure privacy protection and to avoid tendencies to dissimulate or respond in a socially desirable direction. A very general model for the RR method was introduced by Franklin (Commun Stat Theory Methods 18:489–505, 1989) when a single-sensitive question is under study. However, since social surveys are often based on questionnaires containing more than a single-sensitive question, the analysis of multivariate RR data is of considerable interest. This paper focuses on the generalization of the Franklin model in a multiple-sensitive question setting and on related inferential issues.

Estimation of population proportion in randomized response sampling using weighted confidence interval construction

This paper considers the problem of estimation for binomial proportions of sensitive attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. By applying the Wilson (J Am Stat Assoc 22:209–212, 1927) score approach for constructing confidence intervals, various probable point estimators and confidence interval estimators are suggested for the common structures of randomized response procedures. In addition, efficiency comparisons are carried out to study the performances of the proposed estimators for both the cases of direct response surveys and randomized response surveys. Circumstances under which each proposed estimators is better are also identified.

Ranked Set Sampling Using Auxiliary Variables of a Randomized Response Procedure for Estimating the Mean of a Sensitive Quantitative Character

The analysis of the behavior of estimators of the mean of a sensitive variable is considered when a randomized response procedure is used. The results deal with the inference based on simple random sampling with replacement study design. A study of the behavior of the procedures for a ranked set sampling design is developed. A gain in accuracy is generally associated with the proposed alternative model.

Bayesian estimation of proportion and sensitivity level in randomized response procedures

A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two-stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non-sensitive group. The randomization is implemented on the basis of Franklin’s procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum-likelihood or moment estimation.

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.

Utilization of higher order moments of scrambling variables in randomized response sampling

In this paper, a new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced. The proposed estimator makes use of higher order moments of the scrambling variable at the estimation stage. The proposed estimator has been found to be more efficient than the estimator due to Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] and Franklin [1989. A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Comm. Statist. Theory Methods 18, 489–505] type estimators in randomized response sampling. Recently, Guerriero and Sandri [2007. A note on the comparison of some randomized response procedures. J. Statist. Plann. Inference 137, 2184–2190] have shown that the family of randomized response models proposed by Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] is better than the Simmons’ family in terms of efficiency and protection.

A unified framework for analysis and comparison of randomized response surveys of binary characteristics

The randomized response (RR) procedures for estimating the proportion ( π ) of a population belonging to a sensitive or stigmatized group ask each respondent to report a response by randomly transforming his/her true attribute into one of several response categories. In this paper, we present a common framework for discussing various RR surveys of dichotomous populations with polychotomous responses. The unified approach is focused on the substantive issues relating to respondents’ privacy and statistical efficiency and is helpful for fair comparison of various procedures. We describe a general technique for constructing unbiased estimators of π based on arbitrary RR procedures, from unbiased estimators based on an open survey with the same sampling design. The technique works well for any sampling design p ( s ) and also for variance estimation. We develop an approach for comparing RR procedures, taking both respondents’ protection and statistical efficiency into account. For any given RR procedure with three or more response categories, we present a method for designing an RR procedure with a binary response variable which provides the same respondents’ protection and at least as much statistical information. This result suggests that RR surveys of dichotomous populations should use only binary response variables.

Repeated Cross-Sectional Randomized Response Data

Randomized response (RR) is an interview technique that can be used to protect the privacy of respondents if sensitive questions are posed. This paper explains how to measure change in time if a binary RR question is posed at several time points. In cross-sectional research settings, new insights often gradually emerge. In our setting, a switch to another RR procedure necessitates the development of a trend model that estimates the effect of the covariate time if the dependent variable is measured by different RR designs. We also demonstrate that it is possible to deal with self-protective responses, thus accommodating our trend model with the latest developments in RR data analysis.

Ranked set sampling and randomized response procedures for estimating the mean of a sensitive quantitative character

This paper is devoted to the analysis of the estimation of the mean of a sensitive variable. The use of a randomized response (RR) procedure gives confidence to the interviewed that his privacy is protected. We consider that a simple random sampling with replacement design is used for selecting a sample. The behavior of the RR procedure, when ranked set sampling is the design used, is developed under three different ranking criteria. The usual gain in accuracy associated with the use of ranked set sampling is exhibited only by one of the designs. The behavior of the models is illustrated using data provided by a study of samples of persons infected with AIDS.

Ratio imputation method for handling item-nonresponse in Eichhorn model

Missing data is often a problem in social science data. Imputation methods fill in the missing responses and lead, under certain conditions, to valid inference. This paper proposes an investigation procedure concerning the Eichhorn and Hayre (6)'s quantitative sensitive characteristic randomized response procedure in the presence of missing data. For the missing randomized responses, their values are imputed in the ratio form. The estimator for the population mean of sensitive characteristic variable is addressed and its nature is discussed in detail. A simulation study evaluates the proposed imputation methods, and this procedure is found to perform well with regards to bias and mean square error.

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, πA, bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for πA, for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.

A design-based randomized response procedure for the estimation of population proportion and sensitivity level

A general design-based approach to randomized response surveys is proposed. The method is tailored for the joint estimation of the proportion of individuals in the population bearing a sensitive attribute and the proportion of individuals in the sensitive group declaring truthfully their status. The proposal is specialized to the case of simple random sampling without replacement, unequal probability sampling without replacement and stratified sampling.