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Abstract.Auxiliary information is widely used in various studies to improve the precision of estimation. In this article, we extend the application of auxiliary information within the context of randomized response techniques (RRT), building upon the prior research on kernel density estimation (KDE) under additive RRT models. Inspired by Mostafa and Ahmad (2019), we proposed a kernel density estimator that incorporates an auxiliary variable to enhance the accuracy of estimating the distribution of a sensitive variable. Extensive simulations are conducted to evaluate the performance of this proposed methodology, highlighting the advantages of utilizing auxiliary information and the impact of factors such as noise levels, sample size, and the correlation between the auxiliary variable and the sensitive variable. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

AbstractDifferent 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). [ABSTRACT FROM AUTHOR]

The key innovation lies in the incorporation of an adaptive cluster sampling strategy and a randomized response model based on the Poisson distribution. This integration aims to overcome shortcomings inherent in conventional models, providing a more robust framework for research area. In this paper, an adaptive cluster sampling randomized response model with Poisson distribution using a randomized response strategy was proposed. The proposed cluster randomized response model has improved efficiency and a large gain in precision. Conditions were obtained under which the proposed model is more efficient than the existing models. To validate the effectiveness of our approach, numerical computations were conducted, offering concrete illustrations of the model's performance. The results underscore the significant gains in efficiency and precision achieved by the proposed adaptive cluster sampling randomized response model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose two types of estimators that are analogous to Franklin's model. One estimator is derived by concentrating on the row averages of the responses, and another is obtained by concentrating on the column averages of the observed responses. In the latter case we have two responses per respondent from a bi‐variate normal distribution. The proposed estimator based on row averages, by making use of negatively correlated random numbers from a multivariate density, is always more efficient than the corresponding Franklin's estimator. In the case of the proposed estimator based on column averages, we found that the use of positively correlated random numbers from a bivariate density can lead to the most efficient estimator. We also discuss results which are observed by making use of three responses per respondent. When the three responses are recorded, three independent normal densities are derived from three correlated variables. The findings are supported based on analytical, numerical, and simulation studies. A simulation study was done to determine the minimum sample size required to produce nonnegative estimates of the population proportion of a sensitive characteristic, and to investigate the 95% nominal coverage by the interval estimates. Ultimately at the end, one best estimator is suggested. A very neat and clean derivations of theoretical results and discussion of numerical and simulation studies are documented in Data S1. [ABSTRACT FROM AUTHOR]

Surveys involving sensitive characteristics entail applying innovative tools such as Randomized Response Techniques (RRTs) to elicit responses from the sampled units. This manuscript proposes one such new two-stage RRT, involving two simple and common randomization devices, namely, a coin and a die. Empirical study has been conducted to show its efficacy over contemporary estimator in terms of both Percentage Relative Efficiency and Privacy Protection. Application of the proposed RRT to election polling has been discussed efficiently. The appropriateness of such application has been illustrated via detailed simulation study. The results have been tabulated and recommendations made for the use of the proposed estimation strategy. [ABSTRACT FROM AUTHOR]

This article proposes two – stage stratified partial randomized response models based on Tracy and Osahan (1995) model and have large gain in precision. It is also shown that the proposed models are more efficient than Kim and Warde (2004) and Kim and Elam (2005) stratified randomized response models under the conditions presented in the case of completely truthful reporting and less than completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study. [ABSTRACT FROM AUTHOR]

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) [ABSTRACT FROM AUTHOR]

To develop more effective interventions, conservationists require robust information about the proportion of people who break conservation rules (such as those relating to protected species, or protected area legislation). Developed to obtain more accurate estimates of sensitive behaviors, including rule‐breaking, specialized questioning techniques such as Randomized Response Techniques (RRTs) are increasingly applied in conservation, but with mixed evidence of their effectiveness. We use a forced‐response RRT to estimate the prevalence of five rule‐breaking behaviors in communities living around the Ruaha–Rungwa ecosystem in Tanzania. Prevalence estimates obtained for all behaviors were negative or did not differ significantly from zero, suggesting the RRT did not work as expected and that respondents felt inadequately protected. To investigate, we carried out a second study to explore how topic sensitivity influenced respondents' propensity to follow RRT instructions. Results from this experimental study revealed respondents understood instructions well (~88% of responses were correct) but that propensity to follow RRT instructions was significantly influenced by the behavior asked about, and the type of answer they were required to provide. Our two studies highlight that even if RRTs are well understood by respondents, where topics are sensitive and respondents are wary of researchers, their use does not necessarily encourage more honest responding. [ABSTRACT FROM AUTHOR]

The randomized response technique is one of the most commonly used indirect questioning methods to collect data on sensitive characteristics in survey research covering a wide variety of statistical applications including, e.g., behavioral science, socio-economic, psychological, epidemiology, biomedical, and public health research disciplines. After nearly six decades since the technique was invented, many improvements of the randomized response techniques have appeared in the literature. This work provides several different aspects of improvements of the original randomized response work of Warner, as well as statistical methods used in the RR problems. [ABSTRACT FROM AUTHOR]

Randomized response techniques (RRTs) are useful survey tools for estimating the prevalence of sensitive issues, such as the prevalence of doping in elite sports. One type of RRT, the unrelated question model (UQM), has become widely used because of its psychological acceptability for study participants and its favorable statistical properties. One drawback of this model, however, is that it does not allow for detecting cheaters—individuals who disobey the survey instructions and instead give self-protecting responses. In this article, we present refined versions of the UQM designed to detect the prevalence of cheating responses. We provide explicit formulas to calculate the parameters of these refined UQM versions and show how the empirical adequacy of these versions can be tested. The Appendices contain R-code for all necessary calculations. [ABSTRACT FROM AUTHOR]

The Randomized Response Technique (Warner, Journal of the American Statistical Association, 60, 63-69, 1965) has been developed to control for socially desirable responses in surveys on sensitive attributes. The Crosswise Model (CWM; Yu et al., Metrika, 67, 251-263, 2008) and its extension, the Extended Crosswise Model (ECWM; Heck et al., Behavior Research Methods, 50, 1895-1905, 2018), are advancements of the Randomized Response Technique that have provided promising results in terms of improved validity of the obtained prevalence estimates compared to estimates based on conventional direct questions. However, recent studies have raised the question as to whether these promising results might have been primarily driven by a methodological artifact in terms of random responses rather than a successful control of socially desirable responding. The current study was designed to disentangle the influence of successful control of socially desirable responding and random answer behavior on the validity of (E)CWM estimates. To this end, we orthogonally manipulated the direction of social desirability (undesirable vs. desirable) and the prevalence (high vs. low) of sensitive attributes. Our results generally support the notion that the ECWM successfully controls social desirability bias and is inconsistent with the alternative account that ECWM estimates are distorted by a substantial influence of random responding. The results do not rule out a small proportion of random answers, especially when socially undesirable attributes with high prevalence are studied, or when high randomization probabilities are applied. Our results however do rule out that random responding is a major factor that can account for the findings attesting to the improved validity of (E)CWM as compared with DQ estimates. [ABSTRACT FROM AUTHOR]

We propose an innovative randomized response estimator that is free from the probabilities of asking the sensitive question and its complement. To utilize the proposed estimator, every respondent uses an independent electronic randomization device, unobserved by the interviewer, which encourages participation by guaranteeing the protection of their privacy. In this paper, such an electronic randomization device is developed, tested through simulation studies, and implemented in a real-world survey. [ABSTRACT FROM AUTHOR]

We propose an improved randomized response model for the simultaneous estimation of population means of two quantitative sensitive variables by using blank card option that make use of one scramble response and another fake response. The properties of the proposed estimator have been analyzed and empirical studies are performed to show its dominance over existing estimators along with enhance privacy protection of the respondents. Suitable recommendations have been made to the survey practitioners. [ABSTRACT FROM AUTHOR]

In the presence of one auxiliary variable and two auxiliary variables, we analyze various exponential estimators. The ranks of the auxiliary variables are also connected with the study variables, and there is a linkage between the study variables and the auxiliary variables. These ranks can be used to improve an estimator’s accuracy. The Optional Randomized Response Technique (ORRT) and the Quantitative Randomized Response Technique are two techniques we utilize to estimate the sensitive variables from the population mean (QRRT). We used the scrambled response technique and checked the proposed estimators up to the first-order of approximation. The mean square error (MSE) equations are obtained for all the proposed ratio exponential estimators and show that our proposed exponential type estimator is more efficient than ratio estimators. The expression of mean square error is obtained up to the first degree of approximation. The empirical and theoretical comparison of the proposed estimators with existing estimators is also be carried out. We have shown that the proposed optional randomized response technique and quantitative randomized response model are always better than existing estimators. The simulation study is also carried out to determine the performance of the estimators. Few real-life data sets are also be applied in support of proposed estimators. It is observed that our suggested estimator is more efficient as compared to an existing estimator. [ABSTRACT FROM AUTHOR]

This article is about making correction in Tarray, Singh, and Zaizai model and further improving it when stratified random sampling is necessary. This is done by using optional randomized response technique in stratified sampling using a combination of Mangat and Singh, Mangat, and Greenberg et al. models. The suggested model has been studied assuming proportional and Neyman allocation schemes. Numerical results show larger gains in efficiency. Through a detailed numerical study, it is established that the suggested model is relatively more efficient than the Kim and Warde model and the models mentioned above. [ABSTRACT FROM AUTHOR]

In survey sampling, to handle the situation where human bias arises due to some personal or illegal questions, the randomized response technique developed by Warner is used [1]. The calibration technique is used to reduce the bias between the original and estimated weights in stratified random sampling. We estimate the population total, using the calibration estimation technique in which the study variable corresponds to a scrambled variable due to the randomized response technique. We have discussed the estimation procedure of population total and suggested some new estimators, such as ratio and exponential estimators, using different distance measures and calibration constraints. The simulation study has been applied tn newly developed estimators in sensitive survey sampling using a scrambled randomized response (SRR). We see that exponential estimators perform better than ratio and simple estimators of the total stratified random samplings when the variable of interest is sensitive. [ABSTRACT FROM AUTHOR]

In recent times, the Bayesian approach to randomized response technique has been used for estimating the population proportion, especially of respondents possessing sensitive attributes such as induced abortion, tax evasion, and shoplifting. This is done by combining suitable prior information about an unknown parameter of the population with the sample information for the estimation of the unknown parameter. In this study, the possibility of using a transmuted Kumaraswamy prior is raised, yielding a new Bayes estimator for estimating the population proportion of sensitive attributes for Warner’s randomized response technique. Consequently, the proposed Bayes estimator with transmuted Kumaraswamy prior is compared with existing Bayes estimators developed with a simple beta and Kumaraswamy priors in terms of their mean square error. The proposed estimator competes well with the existing estimators for some values of population proportion π. The performances of Bayes estimators were also compared using some benchmark data. [ABSTRACT FROM AUTHOR]

The prevalence of illicit drug use among high school students living in the Silesian voivodship (Poland) is estimated using either the random response techniques of forced response design or the Liu-Chow method. Respondents answer a sensitive question only with a certain probability, thus ensuring anonymity. These methods provide correct estimates of prevalence, unlike interviews based on anonymous questionnaires, which can lead to underestimate the prevalence. Compared with those obtained with anonymous questionnaires, the results obtained with the forced response method are that 10.7 times more high school students used the new psychoactive substances, 6.0 times more amphetamines, methamphetamines, and others, 3.1 times more heroin or morphine, and 1.6 times more marijuana or hashish. The Liu-Chow method provides an estimate of 10.7% of respondents who reported using new psychoactive substances, while the estimate by the anonymous questionnaire is only 1.5%. In the case of marijuana or hashish, the Liu-Chow method gives an estimate of 37.0% of users, while the estimate with anonymous questionnaires is only 22.0%. [ABSTRACT FROM AUTHOR]

Getting correct answers to sensitive questions from the respondents and estimating the population parameters on variables that are sensitive in nature is prevailing problem in survey sampling. In the present research paper, the problem of estimation of the population proportion of sensitive characteristics has been studied. For this, an improved randomized response device has been developed by taking the two cases of the unrelated question, case-I: 'when the proportion of unrelated characteristic is known' and other case-II: 'when the proportion of unrelated characteristic is not known'. Two estimators of the population proportion of a sensitive characteristic have been proposed, one for a known value of unrelated characteristic π y and the other for an unknown value, which were found to be unbiased. The expression for variances and unbiased estimates for the variances of the proposed estimators have been obtained. The optimum value of sample sizes has been worked out for which the minimum variance for the proposed estimators has also been obtained. An empirical study has been conducted and concluded graphically that proposed estimators are better than the estimators of Mangat (1992) and Tiwari and Mehta (2016). [ABSTRACT FROM AUTHOR]

The illegal use of natural resources, manifested in activities like illegal logging, poaching, and illegal wildlife trade, poses a global threat to biodiversity. Addressing them will require an understanding of the magnitude of and factors influencing these activities. However, assessing such behaviors is challenging because of their illegal nature, making participants less willing to admit engaging in them. We compared how indirect (randomized response technique) and direct questioning techniques performed when assessing non‐sensitive (fish consumption, used as negative control) and sensitive (illegal consumption of wild animals) behaviors across an urban gradient (small towns, large towns, and the large city of Manaus) in the Brazilian Amazon. We conducted 1,366 surveys of randomly selected households to assess the magnitude of consumption of meat from wild animals (i.e., wild meat) and its socioeconomic drivers, which included years the head of household lived in urban areas, age of the head of household, household size, presence of children, and poverty. The indirect method revealed higher rates of wildlife consumption in larger towns than did the direct method. Results for small towns were similar between the two methods. The indirect method also revealed socioeconomic factors influencing wild meat consumption that were not detected with direct methods. For instance, the indirect method showed that wild meat consumption increased with age of the head of household, and decreased with poverty and years the head of household lived in urban areas. Simultaneously, when responding to direct questioning, households with characteristics associated with higher wild meat consumption, as estimated from indirect questioning, tended to underreport consumption to a larger degree than households with lower wild meat consumption. Results for fish consumption, used as negative control, were similar for both methods. Our findings suggest that people edit their answers to varying degrees when responding to direct questioning, potentially biasing conclusions, and indirect methods can improve researchers' ability to identify patterns of illegal activities when the sensitivity of such activities varies across spatial (e.g., urban gradient) or social (e.g., as a function of age) contexts. This work is broadly applicable to other geographical regions and disciplines that deal with sensitive human behaviors. [ABSTRACT FROM AUTHOR]

In the era of survey sampling, there is an increasing interests in sensitive features of the population that people generally prefer to hide from people. A novel technique called the Randomized Response Technique (RRT)is used to gather reliable data, protectthe confidentiality of respondents, and estimate the population proportion, bearing the sensitive attribute. But the perception of sensitivity is notthe same for every person. It has been observed that a group of people are willing to disclose their true nature rather than the compulsory Randomized Response (RR). Considering this fact, the concept of optional RRT was developed.In the present work, we reformulate an estimation method of sensitive population proportion addressed by Singh, Singh, Mangat and Tracy s’two-stage RRT. The procedure is more generalized here when respondents are chosen exclusively byan unequal probabilitysampling scheme and an unbiased estimator is derived along with its unbiased variance estimator. Further, we develop an Optional Randomized Response (ORR) method based on our proposed work. A simulation study has been carried out to find out the efficacy of the proposed RR and ORR procedures. [ABSTRACT FROM AUTHOR]

In this article Warner (1965) randomized response model is used to determine the allocation of sample sizes in stratified sampling design. The problem is formulated as Nonlinear Programming Problem (NLPP) with non linear cost function. The formulated problem is solved using Branch and Bound method and the results are obtained through LINGO. [ABSTRACT FROM AUTHOR]

This paper aims to introduce Randomized Response Techniques (RRT’s) and show that how RRT’s are implemented in surveys in which sensitive behaviors are investigated. For this purpose, the most popular designs of the Binary RRT are summarized and an experimental study is conducted on drug use among dormitory students at a public university in Ankara, Turkey. Despite the wide applicability of the drug use studies in Turkey, surprisingly any applications using indirect questioning techniques are not observed in the literature. In this study, for the first time, drug use behavior is investigated with Crosswise design which is the most frequently used indirect questioning technique and indirect questioning method (Crosswise design) is compared with direct questioning method to evaluate the effectiveness of the RRT. Results revealed that when Crosswise design is provided on asking sensitive questions, considerably minor response refusals are happened and significantly higher drug-use estimates are observed. [ABSTRACT FROM AUTHOR]

Der vorliegende Beitrag geht der Frage nach, wie das Ausmaß von Schwarzarbeit in Deutschland im Rahmen von Befragungen der allgemeinen Bevölkerung mçglichst valide geschätzt werden kann. In einem experimentellen Design wird die konventionelle direkte Befragungstechnik mit zwei Spezialtechniken, der Randomized-Response- Technik (RRT) und der Item-Count-Technik (ICT), verglichen. Die RRTund die ICT wurden für die Messung besonders heikler Verhaltensweisen entwickelt und sollen durch eine Erhçhung der Anonymität in der Interviewsituation sozial erwünschtes Antwortverhalten reduzieren. Unsere Befunde zeigen, dass die häufig angenommene Wirkung der beiden Spezialtechniken auf die Bereitschaft der Befragten, sozial unerwünschtes Verhalten zu berichten, nicht eindeutig ausfällt. Zudem werden theoretisch bedeutsame Einflussfaktoren von Schwarzarbeit diskutiert und deren Wirkung im Rahmen von multiplen Regressionsanalysen empirisch überprüft. Neben Gelegenheitsstrukturen sind vor allem soziale Normen gute Prädiktoren für die individuelle Entscheidung schwarzzuarbeiten. This article explores methods used to obtain a higher validity in estimates of the prevalence of undeclared work in Germany in surveys within the general population. Using an experimental design two "dejeopardizing" techniques are compared as alternatives to direct questioning when asking sensitive questions: the randomized response technique (RRT) and the item count technique (ICT). These techniques were specifically developed to reduce misreporting on sensitive topics: The goal is to elicit a higher proportion of honest answers from respondents by increasing the anonymity of the question-and-answer process. Our results suggest that neither RRT nor ICT provide unambiguous results with respect to more successful elicitation of reports of socially undesirable behavior. In addition, the theoretically significant influence of background variables is investigated empirically by means of multiple regression. Factors which foster illicit work are, aside from opportunity structures, social norms, which contribute significantly to the explanation of individual decisions to engage in undeclared work. [ABSTRACT FROM AUTHOR]

This paper addresses the estimation of the mean number of individuals in the population who possess a rare sensitive attribute using Poisson distribution for the situations of (i) clustered population and (ii) stratified population with clusters are strata units. Properties of the proposed estimation procedures have been discussed when the proportion of a rare unrelated non-sensitive attribute is assumed to be known as well as unknown. Empirical studies are carried out to support the theoretical results which showed dominance over Lee et al. [Estimation of a rare sensitive attribute in probability proportional to size measures using Poisson distribution. Statistics (Ber). 2014;48(3):685-709] estimation procedures. [ABSTRACT FROM AUTHOR]

This study focuses on the estimation of population mean of a sensitive variable in stratified random sampling based on randomized response technique (RRT) when the observations are contaminated by measurement errors (ME). A generalized estimator of population mean is proposed by using additively scrambled responses for the sensitive variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The performance of the proposed estimator is evaluated both theoretically and empirically. Results are also applied to a real data set. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient stratified randomized response model based on Chang et al.'s (2004) model. We have obtained the variance of the proposed estimator of πs, the proportion of the respondents in the population belonging to a sensitive group, under proportional and Neyman allocations. It is shown that the estimator based on the proposed model is more efficient than the Chang et al.'s (2004) estimator under both proportional as well as Neyman allocations, Hong et al.'s (1994) estimator and Kim and Warde's (2004) estimator. Numerical illustration and pictorial representation are given in support of the present study. [ABSTRACT FROM AUTHOR]

In this paper, we improve the efficiency of Koyuncu et al (2014)'s estimator of population mean of sensitive variable by replacing Traditional Randomized response technique with Optional Randomized response technique as suggested by Gupta et al (2014). The mean square error of proposed estimator is obtained, up to first order of approximation, and is compared with mean square error of various existing estimators theoretically as well as numerically. [ABSTRACT FROM AUTHOR]

Understanding violations of laws or social norms designed to protect natural resources from overexploitation is a priority for conservation research and management. Because direct questioning about stigmatized behaviors can produce biased responses, researchers have adopted more complex, indirect questioning techniques. The randomized response technique (RRT) is one of the most powerful indirect survey methods, yet analyses of these data require sophisticated statistical models. To date, there has been limited user‐friendly software to analyze RRT data, particularly for models that combine information from multiple RRT questions. We developed an R package, zapstRR (ZoologicAl Package for RRT) that provides functions for 3 RRT models that can be applied to single or multiple RRT questions. With these functions, researchers can estimate the prevalence of conservation noncompliance, determine the number of violations by individuals, perform regressions for univariate and multivariate RRT data, and correct prevalence estimates for evasive‐response bias. We illustrate the use of these estimators for RRT data through an examination of 2 case studies: illegal bird hunting where the interview consisted of a standard RRT question design and a novel implementation designed to offer further anonymity to respondents and reveal the impact of educational interventions on illegal bushmeat consumption. The case studies demonstrate how the models can work in tandem to uncover distinct patterns within RRT data sets. The case studies also show how several assumptions are central to the application of the multivariate models. Article impact statement: Data derived from the randomized response technique can be analyzed with a user‐friendly R package. [ABSTRACT FROM AUTHOR]

Randomized response techniques (RRTs) have been proposed in survey sampling literature as a solution to the problem of social desirability bias (SDB) while dealing with sensitive questions. All RRTs reduce the SDB by introducing privacy protection for the respondents, but the variances of the estimates become larger comparedwith the ones obtained from direct questioning technique (DQT). The success of RRTs heavily depends on the assumption that the variable of interest is in fact sensitive for the population under study. There might be situations, however, where a presumably sensitive question is not considered to be sensitive in some populations, in which case using an RRT instead of the DQT would inflate the variance of the estimates unreasonably. In this study, we propose a two-stage sampling procedure for a binary response, which enables one to accurately estimate both the prevalence of the sensitive characteristic and the probability of cheating in a population. The proposed model allows one to choose between an RRT and the DQT.We support our theoretical results with numerous simulations. [ABSTRACT FROM AUTHOR]

This work proposes a general class of estimators for the population total of a sensitive variable using auxiliary information. Under a general randomized response model, the optimal estimator in this class is derived. Design‐based properties of proposed estimators are obtained. A simulation study reflects the potential gains from the use of the proposed estimators instead of the customary estimators. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Collecting reliable responses to sensitive survey questions is challenging, since respondents may be more likely to refuse to respond or to provide biased responses. To address these challenges, Warner (J Am Stat Assoc 60:63–69, 1965) pioneered the randomized response (RR) technique to estimate proportions of individuals in a population with either of two possible attributes. The RR technique can overcome non-response and underreporting biases because it doesn’t reveal the respondent’s attribute, and a generalization of the random component of the response by Christofides (Metrika 57:195–200, 2003) improves estimation properties. In this study, we develop a new RR model to estimate proportions of individuals with each of multiple categories of an attribute using a single sensitive question by means of only one randomization device based on Christofides’s (Metrika 57:195–200, 2003) model. Under the proposed model, a respondent reports the absolute difference between an integer associated with his or her attribute and a random integer. In a part of this research, we conduct a simulation study of the relative efficiency of the proposed methods. The technique is illustrated using data from the 2012 Family and Gender Module of the Taiwan Social Change Survey to estimate the proportions of individuals of different sexual orientations, and the results are compared with the results of direct inquiry from the same survey. [ABSTRACT FROM AUTHOR]

This article addresses the problem of estimating the proportion πS 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. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the population total of the sensitive variable under a unified approach. Odumade and Singh (2008) have suggested a forced quantitative randomized response model and then suggested an unbiased estimator of the population total Y of the sensitive variable y. It is observed that the optimum estimator of the population total Y due to Odumade and Singh (2008) depends on the unknown population parameter under investigation which lacks the practical utility. To overcome this drawback Odumade and Singh (2008) suggested another unbiased estimator of the population total of the sensitive variable based on two independent samples which causes the increase in the cost. Keeping this in view we define an alternative randomized response procedure and hence the estimator of the population total of the sensitive variable based on one sample only which is free from such limitation and more efficient than the Odumade and Singh (2008) estimator. The relative efficiency of the proposed estimator with respect to Bar-Lev et al. (2004) and Odumade and Singh (2008) estimators are examined through numerical illustration. [ABSTRACT FROM AUTHOR]

The crux of this article is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1991) randomization device by utilizing the Poisson distribution in simple random sampling and stratified sampling. Properties of the proposed randomized response (RR) model have been studied along with recommendations. It is also shown that the proposed model is more efficient than that of Land et al. (2011) in simple random sampling and that of Lee et al. (2013) in stratified random sampling when the proportion of persons possessing a rare unrelated attribute is known. Numerical illustrations are also given in support of the present study. [ABSTRACT FROM AUTHOR]

The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1992) randomization device by utilizing the Poisson distribution in survey sampling. It is shown that the proposed model is more efficient than Land et al. (2011) when the proportion of persons possessing a rare unrelated attribute is known. Properties of the proposed randomized response model have been studied along with recommendations. We have also extended the proposed model to stratified random sampling on the lines of Lee et al. (2013). It has been also shown that the proposed estimator is better than Lee et al.'s (2013) estimator. Numerical illustrations are also given in support of the present study. [ABSTRACT FROM PUBLISHER]

This paper applies stratified random sampling using Neyman allocation to Mangat et al. (1992) unrelated question randomized response (RR) strategy for both completely truthful reporting and less than completely truthful reporting. It is shown that, for the prior information given, our new model is more efficient in terms of variance (in the case of completely truthful reporting) and mean square error (in terms of less than completely truthful reporting) than Kim and Elam's (2007) model. Numerical illustrations and graphs are also given in support of the present study. [ABSTRACT FROM PUBLISHER]

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1--P) for a given probability sampling design under Warner's (1965) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each. [ABSTRACT FROM AUTHOR]

Economic games offer a convenient approach for the study of prosocial behavior. As an advantage, they allow for straightforward implementation of different techniques to reduce socially desirable responding. We investigated the effectiveness of the most prominent of these techniques, namely providing behavior-contingent incentives and maximizing anonymity in three versions of the Trust Game: (i) a hypothetical version without monetary incentives and with a typical level of anonymity, (ii) an incentivized version with monetary incentives and the same (typical) level of anonymity, and (iii) an indirect questioning version without incentives but with a maximum level of anonymity, rendering responses inconclusive due to adding random noise via the Randomized Response Technique. Results from a large (N = 1,267) and heterogeneous sample showed comparable levels of trust for the hypothetical and incentivized versions using direct questioning. However, levels of trust decreased when maximizing the inconclusiveness of responses through indirect questioning. This implies that levels of trust might be particularly sensitive to changes in individuals' anonymity but not necessarily to monetary incentives. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

In this paper we have suggested a class of unbiased estimators of πS, the proportion of respondents possessing a sensitive attribute A using mixed randomized response model. The variance of the proposed class of estimators has been obtained. In addition to Kim and Warde's (2005) estimator, several other acceptable estimators of πShave been identified from the proposed class for suitable weights. It has been shown that the newly identified estimators are more efficient than the Kim and Warde's (2005) estimator. Numerical illustrations and graphs are also given in support of the present study. [ABSTRACT FROM AUTHOR]