Question Randomized Response Model Research Articles

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.

A Two-Stage Unrelated Question Randomized Response Model for Estimating the Prevalence of Stigmatized Attribute

The randomized response technique (RRT) is an effective method designed to obtain the stigmatized information from respondents while assuring the privacy. In this study, we propose a new two-stage unrelated question RRT model to estimate the prevalence of sensitive attribute π when the proportion of unrelated innocuous attribute is known and unknown. A simulation study is carried out to validate the theoretical results of proposed estimators. The utility of proposed two-stage unrelated question RRT model under stratification is also explored. An efficiency comparison between the proposed two-stage unrelated question RRT model and the Singh and Suman RRT model is carried out numerically under simple and stratified random sampling.

Two sensitive characteristics and their overlap with two questions per card

AbstractIn this paper, we developed a new unique unrelated question randomized response model in which each card has two questions, either both questions on the sensitive characteristics or both questions on the two unrelated characteristics. The proposed model is unique in the sense this is the only way of asking two questions printed on each card that leads to protection of the privacy of the respondent. We first develop estimators of the prevalence of the two sensitive characteristics and of their overlap. Then we show that the resultant estimators are unbiased. Next we derive variance expressions for the developed estimators of the proportions. We also compute the relative efficiency and relative privacy protection of the proposed model with respect to its competitors. The variances of the proposed estimators are also verified by comparing them to the Cramer–Rao lower bounds of variance–covariance of the estimators. Estimators of conditional proportion, relative risk, and correlation coefficient are also discussed. Lastly, a real data application of the proposed model is considered, which shows the importance of the use of the proposed model in medical and social science studies.

A two-stage unrelated question randomized response model for estimating the rare sensitive parameter under Poisson distribution

In this paper, we propose a new two-stage unrelated question randomized response technique (RRT) model to estimate the mean of the number of persons possessing a rare sensitive attribute using the Poisson distribution. The utility of proposed two-stage unrelated question RRT model under stratification is also explored. Efficiency comparison between proposed two-stage unrelated question and Singh and Suman (2019) RRT model is carried out numerically under simple random sampling, and with Suman and Singh (2019) in stratified random sampling, respectively.

Corrected estimator of sensitive population proportion using unknown repeated trials in the unrelated question randomized response model.

In this paper, we have pointed out a major mistake in the research paper of Singh and Mathur [(2004). Unknown repeated trials in the unrelated question randomized response model, Biometrical Journal, 46:375-378]. We have corrected this mistake and proposed the corresponding corrected estimator of sensitive population proportion. Furthermore, we have obtained the variance of our proposed estimator. Likewise, Singh and Mathur, we have also compared the variance of our proposed estimator with that of the Greenberg etal.'s estimator theoretically as well as numerically.

An improved unrelated question randomized response model

An improved unrelated question randomized response model

Shrinkage Estimation Procedure of Population Mean with Stigmatizing Character in Unrelated Question Randomized Response Technique

This work deals with the estimation of population mean related to sensitive characteristic. A shrinkage estimator of population mean using a prior information is proposed under unrelated question randomized response model where one of the two questions presented to the respondents is non-stigmatized and unrelated to the stigmatized character. The properties of proposed estimator have been discussed, and empirical studies are accomplished to demonstrate the performance of the proposed estimation procedure.

A Stratified and Two Sample Stratified Conditional Unrelated Question Model

본 논문에서는 모집단이 층으로 구성되어 있고 얻고자 하는 속성이 민감할 때, 덜 민감한 속성 B와 강요응답으로 구성되어 있는 확률장치를 통해 “예”라고 응답한 사람들에게만 민감한 속성 A와 무관한 속성 Y를 포함하고 있는 Greenberg et al.(1969)의 무관질문모형을 사용하도록 하여 모집단이 층화된 경우 층화추정을 위한 층화 조건부 무관질문모형을 제안하였다. 그리고 제안한 층화 조건부 무관질문모형에서 각 층에 표본을 배분할 때 비례배분과 최적배분 문제를 다루었다. 또한 층화 조건부 무관질문모형을 무관한 속성이 미지인 경우 두 개의 독립표본을 이용하는 층화 이표본 조건부 무관질문모형으로 확장하였으며, 제안한 층화 이표본 조건부 무관질문모형의 두 번째 단계에서 사용되는 h층의 표본의 크기에 대한 최적값을 도출하여 최소분산을 구하였다. 마지막으로 층화 조건부 무관질문모형이 층화 무관질문모형과 층화 Carr et al.(1982)의 모형보다 효율적이 되는 조건을 제시하여 일정한 조건하에서 제안한 모형이 기존 모형들보다 효율적임을 보였으며, 제안한 층화 조건부 무관질문모형이 π_h₂값이 작고 π_hy값이 작을수록 층화 Carr et al.(1982)의 모형보다 효율적임을 수치적으로 보였다.We suggest a stratified conditional unrelated question randomized response model to more efficiently estimate a sensitive character A when the population is composed of several strata. In that model, only the respondents who answered “yes” through randomization device which was consisted of a less sensitive character B and a question forcing to answer “yes” respond to our suggested model and we deal with two allocation problems of proportional allocation and optimal one. We expand the suggested model into two sample stratified conditional unrelated question model to cover the case of unknowing unrelated character and deduce minimal variance through optimal sample size of stratum h. Finally, we show that the suggested model is more efficiency than stratified unrelated models and the stratified Carr et al.’s model (1982) under some given conditions, and show numerically that the smaller the values π_h₂ and π_hy, the more efficiency the fit of the model.

3단계 무관질문모형에 의한 드문 민감한 속성의 확률비례 추정

최근 Land et al.(2011)은 무관질문모형을 활용하여 드문 민감한 속성(rare sensitive attributes)을 가지고 있는 사람들의 수 평균을 추정하는 방법으로 포아송분포를 이용하는 방안을 제안하였다. 그들은 드문 민감한 속성과 드문 무관한 속성을 이용하여 드문 민감한 속성에 대한 정보를 얻어내고 있다. 본 연구에서는 조사하고자 하는 내용이 매우 민감하고 모집단이 크기가 서로 차이가 있는 집락으로 구성되어 있을 때, 집락의 크기를 고려하여 추출확률을 부여하는 확률비례추출법을 Land et al.(2011)이 사용한 무관질문모형 대신에 3단계 무관질문모형에 적용하여 드문 민감한 속성을 효율적으로 추정하는 방법을 제안하였다. 드문 무관한 속성의 모비율을 알 때, 확률비례 추출 및 등확률 2단계 추출법을 적용하여 드문 민감한 속성에 대한 추정량과 그 분산 및 분산추정량을 구하였다. 그리고 확률비례 복원추출법과 확률비례 비복원추출법에 의해 얻어진 드문 민감한 속성의 추정량과 등확률 2단계 추출법에 의해 얻어진 드문 민감한 속성의 추정량간의 효율성을 비교하였다. 그 결과 집락의 크기가 서로 차이가 있을 때는 확률비례복원추출에 의한 추정이 등확률 복원 2단계 추출에 의한 추정보다 효율이 높아짐을 확인할 수 있었다.Land et al. (2011) have suggested a method to estimate the mean number of persons possessing a rare sensitive attribute by utilizing the Poisson distribution in survey sampling. They obtain information about a rare sensitive attribute through unrelated question randomized response model which is made of a rare sensitive and unrelated attribute. In this paper, we suggest an efficient method of estimating a rare sensitive attribute by using three-stage unrelated randomized response model instead of the Land et al.’s model (2011) when the population consists of some different sized clusters and clusters are selected by probability proportional to size (pps) sampling. Under the assumption that the parameter of a rare unrelated attribute is known, we estimate the parameter of a rare sensitive attribute and it’s variance and variance estimator. We compare the efficiency of our suggested pps estimation method with equal probability two-stage sampling method and ascertain that the estimation by pps with replacement is more efficiency than equal probability two-stage sampling with replacement.

A new efficient unrelated randomized response model

ABSTRACTThe present paper suggests an interesting and useful ramification of the unrelated randomized response model due to Pal and Singh (2012) [A new unrelated question randomized response model. Statistics 46 (1), 99–109] that can be used for any sampling scheme. We have shown theoretically and numerically that the proposed model is more efficient than Pal and Singh (2012) model.

A stratified unrelated question randomized response model using Neyman allocation

ABSTRACTThis 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.

A sinuous stratified unrelated question randomized response model

ABSTRACTThis paper considers the use of stratified random sampling with proportional as well as Neyman allocations to unrelated question randomized response strategy. It has been 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 case of less than completely truthful reporting). Numerical illustrations are also given in support of the present study.

A randomized response model for estimating a rare sensitive attribute in stratified sampling using poisson distribution

The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Singh et al. (1) randomization device by utilizing the Poisson distribution in stratified sampling. This study also deals with the extension of the estimation reported by Singh and Tarray (2) using a Poisson distribution and an unrelated question randomized response model reported in Singh et al. (1). In stratified sampling, the estimators are proposed when the parameter of the rare unrelated attribute is known and also when it is unknown. It is shown that the proposed models are more efficient than the model given by Lee et al. (3) in both cases, that is, when the proportion of persons possessing a rare unrelated attribute is known and that when it is unknown. When the sizes of the stratified populations are not given, other estimators are suggested using stratified double sampling. Properties of the proposed randomized response model are studied and recommendations are made.

An Adroit Stratified Unrelated Question Randomized Response Model using Neyman Allocation

In this paper we consider the use of stratified random sampling with Neyman allocation to Singh et al. (1994) unrelated question randomized response strategy for completely truthful reporting. It has been shown that for the prior information given, our new model is more efficient in terms of variance (in the case of completely truthful reporting) than Kim and Elam’s (2007) model. Numerical illustrations and graphs are also given in support of the present study. DOI: http://dx.doi.org/10.4038/sljastats.v15i2.7409

Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution

This study proposes the estimators for the mean and its variance of the number of respondents who possessed a rare sensitive attribute based on stratified sampling schemes (stratified sampling and stratified double sampling). This study deals with the extension of the estimation reported in Land et al. [Estimation of a rare sensitive attribute using Poisson distribution, Statistics (2011), in press. DOI: 10.1080/02331888.2010.524300] using a Poisson distribution and an unrelated question randomized response model reported in Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), 520–539]. In the stratified sampling, the estimators are proposed when the parameter of the rare unrelated attribute is known and unknown. The variances of estimators using a proportional and optimum allocation are also suggested. The proposed estimators are evaluated using a relative efficiency comparing variances of the estimators reported in Land et al. depending on the parameters and the probability of selecting a question. We showed that our proposed methods have better efficiencies than Land et al.’s randomized response model in some conditions. When the sizes of stratified populations are not given, other estimators are suggested using a stratified double sampling. For the proportional allocation, the difference between two variances in the stratified sampling and the stratified double sampling is given with the known rare unrelated attribute.

A new unrelated question randomized response model

In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied.

An improved procedure for estimation of proportion of a sensitive attribute of the population

In this paper, we have suggested a family of estimators ˆ πW for estimating π, the proportion of population having sensitive category, under unrelated question randomized response model. It is shown that the suggested class of estimators ˆ πW of

A stratified unrelated question randomized response model

This paper presents a new randomized response model that combines Kim and Warde's (2004) stratified Warner's randomized response technique using optimal allocation with the unrelated question randomized response model. The empirical studies performed show that, for the prior information given, the new model is more efficient in terms of variance (in the case of completely truthful reporting) and mean square error (in the case of less than completely truthful reporting) than its component models.

Unknown Repeated Trials in the Unrelated Question Randomized Response Model

AbstractThis paper proposes a modified randomization device for collecting information on sensitive issues. The estimator based on the suggested strategy is found to be unbiased for population proportion and is better than the Greenberg et. al.'s (1969) estimator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An alternative device for randomized responses

The present study considers an alternate randomization device in unrelated question randomized response model. The proposed model based estimator is unbiased for population proportion and is always more efficient than Greenberg et al. (1969) usual estimator. The conditions under which the proposed model is superior to Mangatts (1991, 1992) recent models have also been obtained.