Two-stage Randomized Response Model Research Articles

An Improved Two-stage Randomized Response Model for Estimating the Proportion of Sensitive 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 RRT model to estimate the prevalence of sensitive attribute ([Formula: see text]). A simulation study shows that the empirical mean and variance of proposed estimator are close to corresponding theoretical values. The utility of proposed two-stage RRT model under stratification is also explored. An efficiency comparison between proposed two-stage RRT model and some existing RRT models is carried out numerically under simple and stratified random sampling.

Randomized response model to alter the nuisance effect of non-response due to stigmatized issues in survey sampling

The present study deals with the estimation procedures of the mean number of persons bearing a rare sensitive attribute in the clustered population under two-stage sampling scheme. The resultant estimators have been suggested using two-stage randomized response model when a rare unrelated attribute is assumed to be known as well as unknown. The properties of resultant estimators are studied where the first-stage samples are drawn using the probability proportional to the size with replacement sampling scheme. The estimation procedures have been further extended for the stratified clustered population. The empirical studies are performed for the validation of the suggested estimation procedures. Recommendations have been made to survey practitioners for their real-life applications.

An ameliorated stratified two-stage randomized response model for estimating the rare sensitive parameter under Poisson distribution

ABSTRACTThis manuscript presents the process for estimating the mean number of individuals having rare sensitive characteristic when population units are heterogeneous with and without prior information on the supplementary (unrelated rare non-sensitive) characteristic. The rare stigmatized parameter is estimated using an ameliorated two-stage randomized response model under stratified sampling and stratified double sampling schemes. The properties of the suggested estimators have been discussed under random, proportional and optimal allocations of sample from different strata. The proposed estimators perform better over some contemporary competent estimators for similar situations which have been shown through empirical studies.

Estimation of a rare sensitive attribute for two-stage randomized response model in probability proportional to size sampling using Poisson probability distribution

ABSTRACTThis 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.

A modified two-stage randomized response model for estimating the proportion of stigmatized attribute

ABSTRACTThe survey related to stigmatized characteristics leads to the non-response problem if it is conducted according to classical (direct) methods, especially, developed for non-sensitive issues; therefore, it needs to be applied appropriate survey methodology to get a reliable response from respondents in incriminating issues. Randomized response model is one of the most recent methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it protects the privacy of individuals in order to acquire the truthful response. The present work proposes a new two-stage randomized response model to get rid of misleading response or non-response due to the stigmatized nature of attribute under the study. The proposed randomized response model results in the unbiased estimator of population proportion possessing the sensitive attribute. The properties of the resultant estimator have been studied and empirical comparisons are performed to show its dominance over existing estimators. Suitable recommendations have been put forward to the survey practitioners.

An improved cluster two-stage randomized response model

ABSTRACTIn this paper, Abdelfatah and Mazloum's (2015) two-stage randomized response model is extended to unequal probability sampling and stratified unequal probability sampling, both with and without replacement. The extended models result in more efficient estimators than Lee et al.'s (2014) estimators of the proportion of the population having a sensitive attribute.

An efficient two-stage randomized response model under stratified random sampling

ABSTRACTA two-stage randomized response model is extended to stratified random sampling in order to find out more efficient estimators of proportions built from sensitive questions, which respondents may not answer truthfully, in a population divided into homogeneous subgroups. In each subgroup, the respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating “yes” or “no”. In the latter case, they are required to report the outcome. Such extension provides a more efficient estimator of the proportion of the population having a given sensitive attribute than its counterpart in simple random sampling. The extended two-stage randomized response model is more efficient than the stratified randomized response model, where respondents must answer the sensitive question either in the first or in the second stage. Moreover, it increases the respondents’ cooperation. When strata weights are unknown, they are estimated by the double sampling method.

A two-stage design for multivariate estimation of proportions

ABSTRACTIn this article, the problem of estimation of the several proportions of two inter-dependent sensitive characteristics prevailing in a given population is considered. A new two-stage randomized response model has been proposed by extending Lee et al.’s (2013) model. The expressions for biases, variances, and mean square errors of different estimators have been provided. The relative efficiency comparisons of the proposed estimators has been made, numerically by considering the different practicable choices of the design parameters. It was observed that the proposed extended version performs efficiently than simple and crossed models of Lee et al. (2013).

Efficient Estimation in a Two-Stage Randomized Response Model

A two-stage randomized response model is devised to circumvent the lack of answers to a sensitive question. Respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating “yes” or “no”. In the latter case, they are required to report the outcome. This apparently innocent device helps to build a more efficient estimator of the proportion of the population having a given sensitive attribute. The procedure also increases the respondents’ cooperation. As other estimators of the proportion of the population having a given sensitive attribute using randomized response models, this estimator can formally take values outside the unit interval, a possibility which should not be allowed. The minimum sample size for which the frequency of estimates outside [0,1] is small enough is obtained by simulation.

A stratified Tracy and Osahan's two-stage randomized response model

ABSTRACTThis paper proposes an alternative two-stage stratified randomized response model based on Tracy and Osahan (1999) model that has an optimal allocation and large gain in precision. It is also shown that the proposed model is more efficient than Kim and Warde (2004) and Kim and Elam (2005) stratified randomized response models under the conditions presented in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study.

Estimation of the proportion of a sensitive attribute based on a two-stage randomized response model with stratified unequal probability sampling

To estimate the proportion of a sensitive attribute of the population that is composed of the number of different sized clusters, we suggest a two-stage randomized response model with unequal probability sampling by using Abdelfatah et al.’s procedure [Braz. J. Probab. Stat. 27 (2013) 608–617]. We compute the estimate of the sensitive parameter, its variance, and the variance estimator for both pps sampling and two-stage equal probability sampling. We extend our model to the case of stratified unequal probability sampling and compute them. Finally, we compare the efficiency of the two estimators, one obtained by unequal probability sampling and the other by stratified unequal probability sampling.

On stratified randomized response sampling

In this paper, we propose a new quantitative randomized response model based on Mangat and Singh (7) two-stage randomized response model. We derive the estimator of the sensitive variable mean, and show that our method is more efficient than other randomized response models suggested by Greenberg et al. (3) and Gupta et al. (4) estimators.

A two-stage stratified Warner?s randomized response model using optimal allocation

This paper applies Kim and Warde’s (2004) stratified Warner’s randomized response model to Mangat and Singh’s (1990) two-stage randomized response model. The proposed stratified randomized response model has an optimal allocation and a large gain in precision. Hence, the estimator based on the proposed method is more efficient than Kim and Warde’s (2004) and Mangat and Singh’s (1990) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.