Maximum likelihood estimation of sensitive proportion using repeated randomized response techniques

Randomized response techniques are designed to obtain usable data on sensitive issues while protecting the privacy of individuals. In this paper, based on repeating the randomized response technique, a new technique called repeated randomized response is introduced to increase the protection of privacy and efficiency of estimator for proportion of sensitive attribute. By using this technique, the proportion of academic cheating is estimated among students of Shahid Chamran University of Ahvaz, Ahvaz, Iran.     

A comparison of two randomized response survey methods with consideration for the level of respondent protection

In recent years randomized response methods have been introduced in an attempt to improve the accuracy and honesty in personalized response surveys of very sensitive questions. Two randomized response methods are compared, taking into account the protection afforded the respondent. In addition, we point out that the estimators, which previous authors have claimed to be the maximum likelihood estimators of the population proportion with the sensitive characteristic, are in fact not the maximum likelihood estimators.     

How to ask sensitive multiple-choice questions

Motivated by recent failures of polling to estimate populist party support, we propose and analyze two methods for asking sensitive multiple-choice questions where the respondent retains some privacy and therefore might answer more truthfully. The first method consists of asking for the true choice along with a choice picked at random. The other method presents a list of choices and asks whether the preferred one is on the list or not. Different respondents are shown different lists. The methods are easy to explain, which makes it likely that the respondent understands how her privacy is protected and may thus entice her to participate in the survey and answer truthfully. The methods are also easy to implement and scale up.     

Ranking responses in multiple-choice questions

In many studies, the questionnaire is a common tool for surveying. There are two kinds of questions designed: single-choice questions and multiple-choice questions. For single-choice questions, the methodology for analyzing it has been provided in the literature. However, the analyses of multiple-choice questions are not established as in depth as those for single-choice questions. Recently, there has been a lot of literature published about testing the marginal independence between two questions involving at least one multiple-choice question. However, another important problem regarding this topic is to rank the responses in a multiple-choice question. The issue is whether there are significant differences in the popularity of particular responses within the same question. In this paper, methodologies for ranking responses are proposed.     

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.     

A stratified randomized response model for sensitive characteristics using non identical trials

Abstract

Stratification provides a powerful tool for improving the efficiency and, being suitable for various sampling situations, it is commonly used in practice. Motivated by the utility of stratified sampling scheme, we focus on studying behavior of the estimator of proportion of a sensitive attribute while dealing with non-identical Bernoulli trials in survey research. The objective is achieved by considering a general randomized response model. Relative efficiency comparisons are presented along with cost analysis by considering different cost functions. Stratified random sampling is observed to be yielding more precise estimators.     

Model selection in randomized response techniques for binary responses

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 compared with 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.     

基于随机化回答模型的最低工资敏感性问题研究

针对最低工资调查中出现的敏感性问题,引入随机化回答技术,并针对定性和定量两类敏感性问题,分别引入不同的随机化回答模型。同时还考虑到最低工资调查中,不同调查单位对同一问题敏感程度不相同的特性,在定量问题的随机化回答模型中引入敏感性水平,对原有模型进行有效的改进,使被调查者能够更加积极配合最低工资调查,从而能够进一步减少由于各类敏感性问题造成的非抽样误差。这套随机化处理方法还可推广应用到其他类型的敏感性问题中。     

Application of Bayesian analyses to doubly randomized delayed start,matched control designs to demonstrate disease modification

Disease modification is a primary therapeutic aim when developing treatments for most chronic progressive diseases. The best treatments do not simply affect disease symptoms but fundamentally improve disease course by slowing, halting, or reversing disease progression. One of many challenges for establishing disease modification relates to the identification of adequate analytic tools to show differences in a disease course following intervention. Traditional approaches rely on the comparisons of slopes or noninferiority margins. However, it has proven difficult to conclusively demonstrate disease modification using such approaches. To address these challenges, we propose a novel adaptation of the delayed start study design that incorporates posterior probabilities identified by hierarchical Bayesian inference approaches to establish evidence for disease modification. Our models compare the size of treatment differences at the end of the delayed start period with those at the end of the early start period. Simulations that compare several models are provided. These include general linear models, repeated measures models, spline models, and model averaging. Our work supports the superiority of model averaging for accurately characterizing complex data that arise in real world applications. This novel approach has been applied to the design of an ongoing, doubly randomized, matched control study that aims to show disease modification in young persons with schizophrenia (the Disease Recovery Evaluation and Modification (DREaM) study). The application of this Bayesian methodology to the DREaM study highlights the value of this approach and demonstrates many practical challenges that must be addressed when implementing this methodology in a real world trial.     

A method for obtaining randomized block designs in preclinical studies with multiple quantitative blocking variables

A method is proposed for block randomization of treatments to experimental units that can accommodate both multiple quantitative blocking variables and unbalanced designs. Hierarchical clustering in conjunction with leaf‐order optimization is used to block experimental units in multivariate space. The method is illustrated in the context of a diabetic mouse assay. A simulation study is presented to explore the utility of the proposed randomization method relative to that of a completely randomized approach, both in the presence and absence of covariate adjustment. An example R function is provided to illustrate the implementation of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

Unbiasedly estimating the total of a stigmatizing variable from a complex survey on permitting options for direct or randomized responses

Following the approach of Mangat and Singh (in J Ind Statist Assoc 32(3): 71–75, 1994) we consider estimating the population total of a sensitive variable like earning through gambling, amount of tax evaded etc. on generating sample responses allowing options for direct or randomized responses according to a specified device. Gathering two independent responses from each individual chosen according to any general sampling scheme we derive unbiased estimators for the total as well as for the variances of these estimators.     

Randomized response multivariate designs for categorical data

Three approaches to multivariate estimation for categorical data using randomized response (RR) are described. In the first approach, practical only for 2×2 contingency tables, a multi-proportions design is used. In the second approach, a separate RR trial is used for each variate and it is noted that the multi­variate design matrix of conditional probabilities is given by the Kroneeker product of the univariate design matrices of each trial, provided that the trials are independent of each other in a certain sense. The third approach requires only a single randomization and thus may be viewed as the use of vector response. Finally, a special-purpose bivariate design is presented.     

数量特征敏感问题问卷设计

目前,数量特征敏感问题调查主要采用随机化策略,该策略需使用随机化装置,从而需要在现场实施。提出一种问卷设计技术,该技术用无关问题替代随机化装置,因而不需要调查者亲临现场,不受调查规模及调查单位聚散的限制,使得调查更加方便、实用、经济。给出了相应的无偏估计量,推算出估计量的方差和方差的估计量并举例说明。     

Robust inference from multiple test statistics via permutations: a better alternative to the single test statistic approach for randomized trials

Formal inference in randomized clinical trials is based on controlling the type I error rate associated with a single pre‐specified statistic. The deficiency of using just one method of analysis is that it depends on assumptions that may not be met. For robust inference, we propose pre‐specifying multiple test statistics and relying on the minimum p‐value for testing the null hypothesis of no treatment effect. The null hypothesis associated with the various test statistics is that the treatment groups are indistinguishable. The critical value for hypothesis testing comes from permutation distributions. Rejection of the null hypothesis when the smallest p‐value is less than the critical value controls the type I error rate at its designated value. Even if one of the candidate test statistics has low power, the adverse effect on the power of the minimum p‐value statistic is not much. Its use is illustrated with examples. We conclude that it is better to rely on the minimum p‐value rather than a single statistic particularly when that single statistic is the logrank test, because of the cost and complexity of many survival trials. Copyright © 2013 John Wiley & Sons, Ltd.     

Adjusted Kuk's model using two non sensitive characteristics unrelated to the sensitive characteristic

In this paper, we adjust the Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions indirectly. Biometrika 77(2):436–438.[Crossref], [Web of Science ®] , [Google Scholar]) model for both protection and efficiency by making use of proportions of two non sensitive characteristics which are unrelated to the main sensitive characteristic of interest. Various situations, where the proportions of the two non sensitive characteristics in the population of interest are known and that when these proportions are unknown, have been investigated. We compared the adjusted model and Kuk's model through a simulation study from both the protection and efficiency points of view.     

On the comparison of Warner's and unrelated question randomized response plans for estimating sensitive finite population proportions

We consider the problem of estimation of a finite population proportion (P) related to a sensitive attribute under Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) randomized response plan and the unrelated question plan due to Horvitz et al. (1967 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) plan with any given value of the plan parameter, there exists an LUE of P based on the unrelated question plan with a uniformly smaller variance for suitable choices of the plan parameters. Assuming that only the attribute is sensitive but its complement is innocuous, the same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same specified level of privacy.     

Randomized Response Techniques Using Maximum Likelihood Estimator

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009) can always be made more efficient than the RR techniques proposed by Warner (1965), Mangat and Singh (1990), and Mangat (1994) by adjusting the proportion of cards in the decks. Arnab et al. (2012) generalized Odumade and Singh strategy (2009) for complex survey designs and wider class of estimators. In this paper improvement of Arnab et al. (2012) estimator has been made by using maximum likelihood method.     

Estimating a distribution for each category of a sensitive variate

The use of a Randomized Response (RR) design makes it possible to estimate the distribution of a sensitive variate. In this paper, the estimation of the distribution of a non-sensitive variate for each category of a sensitive variate is considered for the case where data on the sensitive variate is obtained by use of an RR procedure. Simple estimators are developed without making any distributional assumptions about the non-sensitive variate. However, if distributional assumptions are made, it is shown that the EM algorithm may be used to compute Maximum Likelihood estimates. Computational comparisons of the estimators, using simulation, indicate that the simple estimators perform well, particularly for large sample sizes.     

A regression estimator for finite population mean of a sensitive variable using an optional randomized response model

Kalucha et al. (Kalucha G., Gupta S., Dass B. K. (accepted). Ratio estimation of finite population mean using optional randomized response models. Journal of Statistical Theory and Practice) introduced an additive ratio estimator for finite population mean of a sensitive variable in simple random sampling without replacement and showed that this estimator performs better than the ordinary mean estimator based on an optional randomized response technique (RRT). In this paper, we introduce a regression estimator that performs better than the ratio estimator even for the modest correlation between the study and the auxiliary variables. A comparison of the proposed estimator with the corresponding ratio estimator and the ordinary RRT mean estimator is carried out theoretically, and is also illustrated with a simulation study.