Randomized Response Procedure Research Articles

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.

Application of setwise randomized response procedures for surveying multiple sensitive attributes.

Application of setwise randomized response procedures for surveying multiple sensitive attributes.

Application of setwise randomized response procedures for surveying multiple sensitive attributes.

Application of setwise randomized response procedures for surveying multiple sensitive attributes.

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.

Asymptotically Optimal Randomized Response Procedures

Abstract An abstract general model of multiway randomized response procedures is investigated, with the aim of minimizing the variance matrix while bounding the risk to which respondents are subjected. A general result on the structure of possible optimal designs is obtained, an improved result is derived for the three-way case, and a complete answer is found for the dichotomous case.

Asymptotically Optimal Randomized Response Procedures

Abstract An abstract general model of multiway randomized response procedures is investigated, with the aim of minimizing the variance matrix while bounding the risk to which respondents are subjected. A general result on the structure of possible optimal designs is obtained, an improved result is derived for the three-way case, and a complete answer is found for the dichotomous case.

Asymptotically Optimal Randomized Response Procedures: An Abstract

This study is concerned with abstract models of randomized response procedures as follows: each individual of the population is assumed to belong to exactly one of the subgroups A1, A2, ..., A,. Observations of discrete random variables X1, X2, ..., X, are made available, and an individual in Ai is to report the value of Xi: let Z be the reported response. Assume simple random sampling with replacement, and independence of the X variables between individuals. The following assumption' is made throughout: if Pj (z) >0 for some j and z, then P, (z) >0. In this case a design can be represented as a set of points (g, (z), ..., gp (z)) in (p 1)-space each with corresponding weight P, (z); here gi (z) = Pj (z)/PP (z). Define an internal point of a design as one which is not an extreme point in the usual sense applied to convex sets: a point is internal if it is a convex combination of others in the design. For a given design, let the risk to an individual in A be measured by R = max P (A i I Z = z) as z varies, and the risk of a design by the vector (R1, ..., RP_1,) or (R1, ..., R,) according to whether we are in Case I (category A, is unembarrassing) or Case II (all categories embarrassing). For general p and unknown nCi only a little more progress can be made. For p = 2, however, it follows that for a given risk as defined above an optimal design exists which can be realised by an unrelated question procedure: in Case I, the usual one considered, the unrelated question should imply the answer yes (the respondent belongs to the sensitive category) with certainty. This is in contrast to earlier recommendations. For nr known exactly, which may sometimes be a convenient assumption during the design stage, the results simplify greatly.

The Randomized Response Technique: A Test on Drug Use

Abstract Eight hundred fifty-four high school students' responses were employed to compare drug-use estimates derived from either (a) traditional direct questioning regarding use of six drugs, or (b) a more indirect and more anonymous method of inquiry, the randomized response procedure. Results indicated that (1) the randomized response procedure produced significantly fewer response refusals, and (2) significantly higher drug-use estimates supported the hypothesized greater sensitivity and validity of the randomized response procedure. The results further suggested that previous estimates derived from standard forms of questioning many have underestimated incidence of drug-use.

The Randomized Response Technique: A Test on Drug Use

Abstract Eight hundred fifty-four high school students' responses were employed to compare drug-use estimates derived from either (a) traditional direct questioning regarding use of six drugs, or (b) a more indirect and more anonymous method of inquiry, the randomized response procedure. Results indicated that (1) the randomized response procedure produced significantly fewer response refusals, and (2) significantly higher drug-use estimates supported the hypothesized greater sensitivity and validity of the randomized response procedure. The results further suggested that previous estimates derived from standard forms of questioning many have underestimated incidence of drug-use.

The Linear Randomized Response Model

Abstract A general linear randomized response model is established with estimates and variances obtained through analogy with familiar linear regression models. All existing randomized response procedures are shown to be special cases of this more general model. Some competing procedures are suggested by the applicability of the model for multivariate mixes of randomized and non-randomized response using either discrete or continuous random variables. Some additional applications are suggested by the applicability of the model for situations where the data have already been collected by some agency but where there are disclosure restrictions.

The Linear Randomized Response Model

Abstract A general linear randomized response model is established with estimates and variances obtained through analogy with familiar linear regression models. All existing randomized response procedures are shown to be special cases of this more general model. Some competing procedures are suggested by the applicability of the model for multivariate mixes of randomized and non-randomized response using either discrete or continuous random variables. Some additional applications are suggested by the applicability of the model for situations where the data have already been collected by some agency but where there are disclosure restrictions.

Application of the Randomized Response Technique in Obtaining Quantitative Data

Abstract The randomized response technique of reducing respondent bias in obtaining answers to sensitive questions is extended from the situation where response is categorical to that in which the response is quantitative. Results are reported on the application of the method to estimating mean number of abortions in an urban population of women, and mean income of heads of households. The efficiency of estimators based on the method of moments in the randomized response procedure is studied and representative results are reported and discussed.