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。     

Privacy protection measures for randomized response surveys on stigmatizing continuous variables

We consider the situation where sample surveys are to be undertaken on sensitive or stigmatizing issues. For such surveys, direct questioning methods usually lead to non-compliance or incorrect responses and so, the randomized response technique, where the responses are collected through some randomization device, is found to be useful. A majority of the literature on these techniques focus on dichotomous sensitive variables, while some techniques are also available for continuous sensitive variables. In this article, we focus on the extent of privacy protection available in sample surveys to respondents for continuous response variables. We also propose two measures of privacy protection. We demonstrate that the parameters of our randomization scheme can be so chosen as to achieve a pre-assigned level of privacy protection while at the same time yielding efficient estimates. We also show some numerical comparisons.     

Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors

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.     

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.     

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.     

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 bayesian comparison of randomized and voluntary response sampling models

This paper is concerned with making a Bayesian comparison between the two types of survey sampling procedures where the individuals are asked sensitive questions. The randomized response procedure is designed to obtain information in such a way that the respondent is protected against revealing his/her status about the sensitive issue. In voluntary response model each individual chooses either to respond or not to respond. It is assumed that the respondents do not falsify their answers. The problem of interest is to estimate the proportion of the sampled population who belong to the sensitive group. A beta prior distribution is used for the proportion of interest. The loss function is taken to be the quadratic loss function.     

Estimation of a sensitive proportion by Warner’s randomized response data through inverse sampling

It is difficult to obtain trustworthy data on stigmatizing matters like habits of tax evasion, drunken driving, etc., through direct queries. To overcome this difficulty, Warner introduced randomized response techniques to estimate the proportion of people bearing such a stigmatizing or sensitive characteristic in a given community. For simplicity in estimation he restricted to SRSWR and since then, several researchers have extended and applied this technique in various ways. All these results involve sampling with a pre-fixed number of draws. In this paper we employ inverse sampling with equal probabilities with replacement and show certain advantages in estimation using randomized response data by Warner’s device gathered through such a simple inverse sampling scheme.     

Generalizations of a contamination model for continuous type random variables

In 1965, Stanley Warner (Warner, 1965) introduced a model for contaminating discrete type random variables. He presented this scheme as being potentially useful in survevs where sensitive in-formation is being gathered. Since that time much research has been conducted and many papers written on the development of these discrete type randomized response models. More recently, atten-tion has been focused on the application of randomized response type models for preservation of confidentiality in existing data files (Boruch 1971 and 1972, Ranney 1975, Felligi 1974, and Inge-marsson 1975). In 1974, Poole (Poole, 1974) introduced a randomized response model for a positive continuous type random variable which was basically a continuous variable analog of the discrete variable Warner model. In this paper the results of the 1974 paper are extended to a lt-dimensional continuous type random variable in k-dimensional Euclidean space.     

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.     

An improved binary randomized response model using six decks of cards

This article purposes the estimation of population proportion of a sensitive attribute through randomized response technique. An efficient estimator is suggested using six decks of cards to randomise the response. Many existing models can now be viewed as the special case of the proposed model. The superiority of the proposed procedure is established through numerical calculation of percentage relative efficiency with prominent competitors. The proposed procedure is also studied under stratified random sampling protocol. In addition, it is shown that, the proposed stratified estimator, performs better in term of efficiency than its only existing two deck stratified competitor.     

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

The 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.     

Likelihood-based Estimation of the Regression Model with Scrambled Responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator out-performs the classical estimators in all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

Improved estimation methods for unrelated question randomized response techniques

The randomized response technique (RRT) is an important tool, commonly used to avoid biased answers in survey on sensitive issues by preserving the respondents’ privacy. In this paper, we introduce a data collection method for survey on sensitive issues combining both the unrelated-question RRT and the direct question design. The direct questioning method is utilized to obtain responses to a non sensitive question that is related to the innocuous question from the unrelated-question RRT. These responses serve as additional information that can be used to improve the estimation of the prevalence of the sensitive behavior. Furthermore, we propose two new methods for the estimation of the proportion of respondents possessing the sensitive attribute under a missing data setup. More specifically, we develop the weighted estimator and the weighted conditional likelihood estimator. The performances of our estimators are studied numerically and compared with that of an existing one. Both proposed estimators are more efficient than the Greenberg's estimator. We illustrate our methods using real data from a survey study on illegal use of cable TV service in Taiwan.     

A RANDOMIZED LONGITUDINAL PLAY-THE-WINNER DESIGN FOR REPEATED BINARY DATA

In some clinical trials with two treatment arms, the patients enter the study at different times and are then allocated to one of two treatment groups. It is important for ethical reasons that there is greater probability of allocating a patient to the group that has displayed more favourable responses up to the patient's entry time. There are many adaptive designs in the literature to meet this ethical constraint, but most have a single binary response. Often the binary response is longitudinal in nature, being observed repeatedly over different monitoring times. This paper develops a randomized longitudinal play‐the‐winner design for such binary responses which meets the ethical constraint. Some performance characteristics of this design have been studied. It has been implemented in a trial of pulsed electro‐magnetic field therapy with rheumatoid arthritis patients.     

Some New Results on the Multinomial Randomized Response Model

ABSTRACT

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.     

Pseudo-Bayes and pseudo-empirical Bayes estimators in randomized response sampling

In this article, new pseudo-Bayes and pseudo-empirical Bayes estimators for estimating the proportion of a potentially sensitive attribute in a survey sampling have been introduced. The proposed estimators are compared with the recent estimator proposed by Odumade and Singh [Efficient use of two decks of cards in randomized response sampling, Comm. Statist. Theory Methods 38 (2009), pp. 439–446] and Warner [Randomized response: A survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc. 60 (1965), pp. 63–69].     

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.     

On randomized response surveys for estimating a proportion

In studies about sensitive characteristics, randomized response (RR) methods are useful for generating reliable data, protecting respondents’ privacy. It is shown that all RR surveys for estimating a proportion can be encompassed in a common model and some general results for statistical inferences can be used for any given survey. The concepts of design and scheme are introduced for characterizing RR surveys. Some consequences of comparing RR designs based on statistical measures of efficiency and respondent’ protection are discussed. In particular, such comparisons lead to the designs that may not be suitable in practice. It is suggested that one should consider other criteria and the scheme parameters for planning a RR survey.