Randomized Response Sampling Research Articles

An unbiased regression type estimator of proportion in randomized response sampling by using analysis of variance mechanism

In this article, two new estimators of population proportion of a sensitive characteristic are introduced by using a method analogous to Analysis of Variance (ANOVA). Then, a new unbiased regression type estimator is developed by utilizing these two estimators. The proposed estimator is, then, compared with its competitor at the same level of protection of the respondents. Also included is a study, based on data collected during summer 2021, of the currently hot topic of estimating the proportion of students, 18 years and older, returning to schools in fall 2021, who tested positive for COVID-19.

A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing sensitive characteristics. However, there is a paucity of research studies that have addressed higher order interactions between these sensitive characters. In this article, we develop a new theory based on three proposed randomized response models which we name as: simple model, semi-crossed model, and fully crossed model. Twenty-one new unbiased estimators of seven parameters are introduced, their variance expressions are derived, and unbiased estimators of variances are developed. The three models are compared under various values of the parameters by computing the percent relative efficiency of one model over another model. The most efficient model is then applied to study the population proportions of three varieties of smoking habits among students, and their first- and second-order interactions. The last four sections (Ninth to Twelfth) are verifications of theoretical results using the Cramer–Rao lower bounds of variances for the developed 21 new estimators in randomized response sampling.

Randomized Response Sampling with Applications to Tracking Drugs for Better Life

Randomized Response Sampling with Applications to Tracking Drugs for Better Life

Lowering the Cramer-Rao lower bounds of variance in randomized response sampling

In this paper, we lower the Cramer-Rao Lower bound of variance due to Singh and Sedory (2011, 2012) for the Odumade and Singh (2009) model in the sense that we propose a randomized response model that is more efficient. We investigate the properties of the proposed model under various situations for protection and efficiency. The adjustment makes use of known proportion of unrelated characteristics. The situation where the proportions of the unrelated characteristics are unknown is also discussed. In addition, we wrote SAS codes to simulate various data sets in order to compute the simulated relative efficiency values.

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.

Forcibly Re-scrambled Randomized Response Model for Simultaneous Estimation of Means of Two Sensitive Variables

Recently, Ahmed et al. (Commun Stat Theory Methods 47(2):324–343, 2018) have introduced the idea of simultaneously estimating means of two sensitive variables by collecting one scrambled response and another pseudo-response. In this paper, we extend their idea to the simultaneous estimation of two means by making use of the forced quantitative randomized response model of Gjestvang and Singh (Metrika 66(2):243–257, 2007) but then re-scrambling the scrambled scores. This idea of re-scrambling already scrambled responses seems completely new in the field of randomized response sampling. The performance of the proposed forced quantitative randomized response model has been investigated analytically as well as empirically.

A generalized procedure for estimating the multinomial proportions in randomized response sampling using scrambling variables

Taking clue from pioneer work of Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012), we have suggested a generalized RR procedure, for estimating the multinomial proportions of potentially sensitive attributes in survey sampling, using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. The RR procedure due to Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012) is viewed as member of the proposed RR procedure. Expressions for variance and covariance of the suggested generalized estimator with its development are derived. It is found that the developed estimator is more efficient than Warner’s (J Am Stat Assoc 60:63–69, 1965) RRT. A numerical illustration is also given in support of the present study.

A new quasi empirical bayes estimate in randomized response sampling

ABSTRACTIn this article, a new notion of “quasi-empirical” Bayes estimation is developed for estimating the proportion of a sensitive attribute in a population by making use of both a prior distribution of prevalence of the sensitive attribute in addition to the known prior distribution of an unrelated characteristic. The proposed quasi-empirical Bayes estimate is compared with those of the unrelated question model due to Greenberg et al. by means of a simulation study.

Alternative Methods to Make Efficient Use of Two Decks of Cards in Randomized Response Sampling

In this article, alternative randomized response models are proposed, which make use of sum of quantitative scores generated from two decks of cards being used in a survey. The proposed methods are compared to the Odumade and Singh and Singh and Grewal models through a simulation study. It is shown that the modified methods can be used more efficiently than those both models.

An extension of Franklin's randomized response technique for multi-proportions

ABSTRACTIn this article, we introduce six estimators, three based on row averages and the remaining three on column averages of population proportions for trichotomous population when randomized response sampling with a normal randomizing distribution is used. The estimators have been obtained using the method of moments. All the proposed estimators are shown to be unbiased and their variances have been worked out. The percent relative efficiencies of the column total based estimators with respect to row total based estimators are investigated through empirical study.

Exact confidence intervals for randomized response strategies

For surveys with sensitive questions, randomized response sampling strategies are often used to increase the response rate and encourage participants to provide the truth of the question while participants' privacy and confidentiality are protected. The proportion of responding ‘yes’ to the sensitive question is the parameter of interest. Asymptotic confidence intervals for this proportion are calculated from the limiting distribution of the test statistic, and are traditionally used in practice for statistical inference. It is well known that these intervals do not guarantee the coverage probability. For this reason, we apply the exact approach, adjusting the critical value as in [10], to construct the exact confidence interval of the proportion based on the likelihood ratio test and three Wilson-type tests. Two randomized response sampling strategies are studied: the Warner model and the unrelated model. The exact interval based on the likelihood ratio test has shorter average length than others when the probability of the sensitive question is low. Exact Wilson intervals have good performance in other cases. A real example from a survey study is utilized to illustrate the application of these exact intervals.

Comparison of Cramer–Rao lower bounds of variances for at least equal protection of respondents

In this paper, a new randomized response model is proposed, which is shown to have a Cramer–Rao lower bound of variance that is lower than the Cramer–Rao lower bound of variance suggested by Singh and Sedory at equal protection or greater protection of respondents. A new measure of protection of respondents in the setup of the efficient use of two decks of cards, because of Odumade and Singh, is also suggested. The developed Cramer–Rao lower bounds of variances are compared under different situations through exact numerical illustrations. Survey data to estimate the proportion of students who have sometimes driven a vehicle after drinking alcohol and feeling over the legal limit are collected by using the proposed randomization device and then analyzed. The proposed randomized response technique is also compared with a black box technique within the same survey. A method to determine minimum sample size in randomized response sampling based on a small pilot survey is also given.

An alternative to stratified Kim and Warde's randomized response model using optimal (Neyman) allocation

This paper addresses the problem of estimating the population proportion πS possessing the sensitive attribute using stratified random sampling. Two alternatives to Kim and Warde [12] stratified randomized response model have been proposed. The proposed models are based on extending Singh [28] mode ls to the case of stratified random sampling. It has been shown that the proposed models are more efficient than Kim and Warde [12] stratified randomized response technique under some realistic conditions in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. A practical problem with the use of optimum (Neyman) allocation has been pointed out. Thus, in practice, the use of either proportional allocation or equal allocation has been suggested while estimating proportion of a sensitive attribute using stratified randomized response sampling. Numerical illustrations and graphs are also given in support of the present study.

Randomized response techniques

Collection of data on sensitive characteristics from human populations is not an easy task. For example sensitive questions: (a) Are you an Alawite? (b) Are you gay? (c) Have you ever molested a child? (d) Have you underreported your income on your tax return? (e) Do you smoke marijuana?, and (f) Have you ever cheated on an exam?, etc. These questions are not likely to be responded honestly by the respondents if they are asked using direct question survey methods. The randomized response technique was first introduced by Warner (1965) to deal with a problem of estimation of such sensitive characteristics in a finite population. This technique enables respondents to provide truthful information in anonymity on sensitive or highly personal questions without endangering their privacy. To promote the pioneer idea of Warner (1965), we have devoted the present issue of the Journal Model Assisted Statistics and Applications on a special topic, “Randomized Response Techniques.” A number of prominent authors who work in the area of randomized response sampling have contributed towards to the special issue, and their details and contributions are explained in brief as follows:

An estimation of a sensitive attribute by two stage stratified randomized response model

We deal with the estimation of sensitive attributeof the population which is composed of a number of strata by applying stratified sampling to Abdelfatah et al.'s model (1). We estimate the sensitive parameter in the case of knowing the size of stratum, and check the effect of the proportional allocation method and the optimum allocation method. We extend it to the case of not knowing the size of stratum, and estimate the sensitive parameter by applying stratified double sampling to Abdelfatah et al.'s model (1). Finally, we compare the efficiency of our suggested estimator to the existing Abdelfatah et al.'s estimator. A practical problem with the use of optimum allocation has been pointed out. Thus, in practice, the use of either proportional allocation or equal allocation has been suggested while estimating proportion of a sensitive attribute using stratified randomized response sampling.

A Stratified Unknown Repeated Trials in Randomized Response Sampling

This paper proposes an alternative stratified randomized response model based on the model of Singh and Joarder (1997). It is shown numerically that the proposed stratified randomized response model is more efficient than Hong et al. (1994) (under proportional allocation ) and Kim and Warde (2004) (under optimum allocation).

A true simulation study of three estimators at equal protection of respondents in randomized response sampling

In this study, three different estimators for estimating the proportion of a sensitive attribute in survey sampling are compared at equal protection of the respondents. The three estimators considered are due to Odumade and Singh (2009, Comm. Statist. Theory Methods), Singh and Sedory (2011, Sociological Methods and Research) and a new estimator obtained by minimizing a chi‐squared distance. A SAS Macro is developed to compare these three estimators using a simulation study at equal protection of the respondents. A set of data from a real face‐to‐face interview was collected using two decks of cards and has been analyzed. The results are discussed.

Estimation of Multinomial Proportions using Higher Order Moments of Scrambling Variables in Randomized Response Sampling

An extension to estimating multinomial proportions of potentially sensitive attributes in survey sampling is proposed using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. The variance and covariance expressions are derived and the relative efficiency of the proposed estimators based on scrambling variables is investigated.

Ranked set sampling and Rao-Hartley-Cochran strategies using the randomized procedure of Ryu-Kim-He-Park

Two Randomized Response sampling models are developed using the scrambling procedure proposed by Ryu-Kim-He-Park are developed. At first we consider the Rao-Hartley- Cochran (RHC) strategy and the estimators of the means is developed. Afterwards Ranked Set Sampling (RSS) design is used and te correpsondign estimators is obtained. The corresponding variances are derived and the efficiency of RSS against RHC procedure is studied.

Cramer-Rao Lower Bound of Variance in Randomized Response Sampling

In this note, the Cramer-Rao lower bound of variance by using the two decks of cards in randomized response sampling has been developed. The lower bound of variance has been compared with the recent estimator proposed by Odumade and Singh at equal protection of respondents. A real practical face-to-face interview data collected using two decks of cards has been analyzed and the results are discussed.