Estimation for sensitive characteristics using optional randomized response technique

This paper considers the problem of procuring honest responses to estimate the population mean of sensitive quantitative characteristics. It aims at pointing out that potential difference between sub-populations seems to be unnoticed under the usual optional randomized response technique. To make an extension to cover all the situations, we propose two alternative survey procedures that enable us to estimate the mean and the variance unbiasedly. Estimation for the sensitivity level of a question is under consideration as well. Efficiency comparisons have also been carried out to study the performances of the proposed procedures.     

A generalized randomized response technique

To eliminate a major source of bias in surveys of human populations resulting from respondents refusal to cooparate in cases where a question of sensitive nature is involved, the idea of “randomized response” was introduced by Warner (1965). In this paper, an alternative randomized response technique is presented which improves upon the pioneering work of Warner (1965). The procedure includes Warner's method as a special case for a specific choice of the parameters. In addition, a generalization of the proposed method is presented.     

An econometric method of correcting for unit nonresponse bias in surveys

Past approaches to correcting for unit nonresponse in sample surveys by re-weighting the data assume that the problem is ignorable within arbitrary subgroups of the population. Theory and evidence suggest that this assumption is unlikely to hold, and that household characteristics such as income systematically affect survey compliance. We show that this leaves a bias in the re-weighted data and we propose a method of correcting for this bias. The geographic structure of nonresponse rates allows us to identify a micro compliance function, which is then used to re-weight the unit-record data. An example is given for the US Current Population Surveys, 1998–2004. We find, and correct for, a strong household income effect on response probabilities.     

An analysis of the effect of pre-incentives and post-incentives based on draws on response to web surveys

Most analyses of the effect of incentives on response rates have attempted to extrapolate to the Internet the already existing broad knowledge base of methodologies for personal surveys by telephone and post. However, such knowledge about existing methods is not directly applicable to the Internet-based interviews. This study therefore examines the manner in which different combinations of incentives can affect response to a survey over the Internet. With such a purpose incentives have been chosen based on draws that has been administered under the pre-incentives philosophy (giving the possibility to participate in a draw, independently that the questionnaire was stuffed or not) or post-incentives (giving the possibility to participate in a draw only those that stuffed the questionnaire). A surprising result is that the joint use of pre-incentives and post-incentives slightly improves response rates, although it also causes rates to be considerably lower than when these incentives are used separately.     

A note on randomized response models for quantitative data

Standard randomized response (RR) models deal primarily with surveys which usually require a yes or a no response to a sensitive question, or a choice for responses from a set of nominal categories. As opposed to that, Eichhorn and Hayre (1983) have considered survey models involving a quantitative response variable and proposed an RR technique for it. Such models are very useful in studies involving a measured response variable which is highly sensitive in its nature. Eichhorn and Hayre obtained an unbiased estimate for the expectation of the quantitative response variable of interest. In this note we propose a procedure which uses a design parameter (controlled by the experimenter) that generalizes Eichhorn and Hayres results. Such a procedure yields an estimate for the desired expectation which has a uniformly smaller variance.Acknowledgements We are grateful to two referees for their valuable and constructive comments.     

Measure of privacy in randomized response model

Randomized response (say, RR) techniques on survey are used for collecting data on sensitive issues while trying to protect the respondents’ privacy. The degree of confidentiality will clearly determine whether or not respondents choose to cooperate. There have been many proposals for privacy measures with very different implications for an optimal model design. These derived measures of protection privacy involve both conditional probabilities of being perceived as belonging to sensitive group, denoted as P(A|yes) and P(A|no). In this paper, we introduce an alternative criterion to measure privacy protection and reconsider and compare some RR models in the light of the efficiency/protection privacy. This measure is known to the respondents before they agree to use the RR model. This measure is helpful for choosing an optimal RR model in practice.     

A strategy for up-dating continuous surveys

Summary The need for regular up-dating of the selection probabilites in continuous surveys is emphasized in this paper. A simple strategy (selection method for the initial sample with the revision procedure) is presented and its application to the Canadian Labour Force Survey is discussed.     

Towards a typology of information to aid reliability of response in social surveys

Covariance structure modelling in the form of a multi-method multitrait model is employed to analyse the reliability of responses to a mail questionnaire sent to young people. A typology of the type of information sought is derived and the model used to test hypotheses about the nature of the reliability of different types of information obtained in the survey.     

Shrinkage estimation of the proportion in randomized response

This article considers the asymptotic estimation theory for the proportion in randomized response survey usinguncertain prior information (UPI) about the true proportion parameter which is assumed to be available on the basis of some sort of realistic conjecture. Three estimators, namely, the unrestricted estimator, the shrinkage restricted estimator and an estimator based on a preliminary test, are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators is presented.     

Randomized response technique for two sensitive characteristics at the same time

In this paper we present a randomized response technique which can be used to estimate the proportion of individuals having two sensitive characteristics at the same time. The information obtained from this procedure can be used for weighting (post-stratification) purposes.     

Constructing optimal randomized response designs with consideration for the level of privacy protection

This paper considers the problem of procuring truthful responses to estimate the proportion of qualitative characteristics. In order to protect the respondent's privacy, various techniques of generating randomized response rather than direct response are available in the literature. But the theory concerning them is generally developed with no attention to the required level of privacy protection. Illustrating two randomization devices, we show how optimal randomized response designs may be achieved. The optimal designs of forced response procedure as well as BHARGAVA and SINGH [Statistica (2000) Vol. 6, pp 315–321] procedure are shown to be special cases. In addition, the equivalent designs of optimal WARNER [Journal of the American Statistical Association (1965) Vol. 60, pp. 63–69] procedure are considered as well. It is also shown that stratification with proportional allocation will be helpful for improving the estimation efficiency.     

Forced quantitative randomized response model: a new device

In the present investigation, a new forced quantitative randomized response (FQRR) model has been proposed. Both situations when the values of the forced quantitative response are known and unknown are studied. The forced qualitative randomized response models due to Liu and Chow (J Am Stat Assoc 71:72–73, 1976a, Biometrics 32:607–618, 1976b) and Stem and Steinhorst (J Am Stat Assoc 79:555–564, 1984) are shown as a special case of the situation when the value of the forced quantitative randomized response is simply replaced by a forced “yes” response. The proposed FQRR model remains more efficient than the recent Bar-Lev et al. (Metrika, 60:255–260, 2004), say BBB model. The relative efficiency of the proposed FQRR model with respect to the existing competitors, like the BBB model, has been investigated under different situations. No doubt the present model will lead to several new developments in the field of randomized response sampling. The proposed FQRR model will encourage researchers/scientists to think more on these lines.     

On the efficiency comparison of certain randomized response strategies

Comparisons between different randomized response strategies have already been performed by several workers but all have concentrated solely on comparing the variances of the appropriate estimators. A very little attention has been paid by these workers to the degree of privacy protection offered to the interviewees. In the present paper, an attempt has been made in this direction and some important randomized response strategies have been compared with the Warner's model, taking into account the aspect of privacy protection. Received February 2000     

An information theoretical algorithm for analyzing supersaturated designs for a binary response

A supersaturated design is a factorial design in which the number of effects to be estimated is greater than the number of runs. It is used in many experiments, for screening purpose, i.e., for studying a large number of factors and identifying the active ones. In this paper, we propose a method for screening out the important factors from a large set of potentially active variables through the symmetrical uncertainty measure combined with the information gain measure. We develop an information theoretical analysis method by using Shannon and some other entropy measures such as Rényi entropy, Havrda–Charvát entropy, and Tsallis entropy, on data and assuming generalized linear models for a Bernoulli response. This method is quite advantageous as it enables us to use supersaturated designs for analyzing data on generalized linear models. Empirical study demonstrates that this method performs well giving low Type I and Type II error rates for any entropy measure we use. Moreover, the proposed method is more efficient when compared to the existing ROC methodology of identifying the significant factors for a dichotomous response in terms of error rates.     

Ranked set sampling and randomized response procedures for estimating the mean of a sensitive quantitative character

This paper is devoted to the analysis of the estimation of the mean of a sensitive variable. The use of a randomized response (RR) procedure gives confidence to the interviewed that his privacy is protected. We consider that a simple random sampling with replacement design is used for selecting a sample. The behavior of the RR procedure, when ranked set sampling is the design used, is developed under three different ranking criteria. The usual gain in accuracy associated with the use of ranked set sampling is exhibited only by one of the designs. The behavior of the models is illustrated using data provided by a study of samples of persons infected with AIDS.     

Admissible unbiased variance estimation in finite population sampling under randomized response

LetP be the proportion of units in a finite population possessing a sensitive attribute. We prove the admissibility of (i) an unbiased estimator of the variance of a general homogeneous linear unbiased estimator ofP and (ii) an unbiased estimator of the population varianceP(1−P), based on an arbitrary but fixed sampling design, under the randomized response plans due to Warner (1965) and Eriksson (1973). Admissibility of an unbiased strategy for estimating the population variance is also established.     

Bayesian estimation of proportion and sensitivity level in randomized response procedures

A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two-stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non-sensitive group. The randomization is implemented on the basis of Franklin’s procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum-likelihood or moment estimation.