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.     

Analysing Misleading Discrete Responses: A Logit Model Based on Misclassified Data*

This study presents an alternative to direct questioning and randomized response approaches to obtain survey information about sensitive issues. The approach used here is based on a logit model that can be used when survey data on the dependent variable are misclassified. The method is applied to a direct survey of undergraduate cheating behaviour. Student responses may not always be truthful. In particular, a student claiming to be a non‐cheater may actually be a cheater. The results indicate that the incidence of cheating in our sample is approximately 70% rather than the self‐reported value of 51%.     

An optional scrambled randomized response technique for practical surveys

Eichhorn and Hayre (J Stat Plan Inference 7:307–316, 1983) introduced the scrambled response technique to gather information on sensitive quantitative variables. Singh and Joarder (Metron 15:151–157, 1997), Gupta et al. (J Stat Plan Inference 100:239–247, 2002) and Bar-Lev et al. (Metrika 60:255–260, 2004) permitted the respondents either to report their true values on the sensitive quantitative variable or the scrambled response and developed the optional randomized response (ORR) technique based on simple random sample with replacement (SRSWR). While developing the ORR procedure, these authors made the assumption that the probability of disclosing the true response or the randomized response (RR) is the same for all the individuals in a population. This is not a very realistic assumption as in practical survey situations the probability of reporting the true value or the RR generally varies from unit to unit. Moreover, if one generalizes the ORR method as developed by these authors relaxing the ‘constant probability’ assumption, the variance of an unbiased estimator for the population total or mean can not be estimated as this involves the unknown parameter, ‘the probability of revealing the true response’. Here we propose a modified ORR procedure for stratified unequal probability sampling after relaxing the assumption of ‘constant probability’ of providing the true response. It is also demonstrated with a numerical exercise that our procedure produces better estimator for a population total than that provided by the method suggested by the earlier authors.     

Estimation of proportion and sensitivity of a qualitative character

In this paper, a simple and obvious procedure is presented that allows to estimate π, the population proportion of a sensitive group, in addition to T, the probability that the respondents belonging to the sensitive group tell the truth whenever questioning directly. Properties of the estimators of π and T as well as sample size allocation are studied. And, efficiency comparisons are carried out to investigate the performance of the proposed method. It is found that the proposed strategy is more efficient than Warner's (1965) strategy, and has an additional advantage of deciding the optimal survey technique for practical situations. Received: October 2000     

How to Improve the Efficiency of Randomised Response Designs

This paper describes ways to maximise the efficiency of randomised response designs. When randomised response designs become more efficient their value as a tool to study sensitive topics will increase. An overview of the literature shows that when sensitive or incriminating topics are studied, the overall results of randomised response studies are more valid than the results of direct question designs. This positive effect is small, however, and randomised response designs are known to be less efficient than direct question designs, making it necessary to recruit larger samples. In this paper the efficiency of six randomised response methods (Warner’s design, both forms of the unrelated question technique, the forced response technique, Moors’s design and Mangat’s improved model) will be compared relative to direct question designs. Using the right design parameters we can make randomised response studies up to twice as efficient. The forced response method and a special form of the unrelated question design are the most efficient designs until now.     

A new privacy-protecting survey design for multichotomous sensitive variables

In this paper, we propose the diagonal model (DM), a survey technique for multicategorical sensitive variables. The DM is a nonrandomized response method; that is, the DM avoids the use of any randomization device. Thus, both survey complexity and study costs are reduced. The DM does not require that at least one outcome of the sensitive variable is nonsensitive. Thus, the model can even be applied to characteristics like income which are sensitive as a whole. We describe the maximum likelihood estimation for the distribution of the sensitive variable and show that the EM algorithm is beneficial to calculate the estimates. Subsequently, we present asymptotic as well as bootstrap confidence intervals. Applying properties of circulant matrices, we show the connection between efficiency loss and the degree of privacy protection (DPP). Here, we prove that the efficiency loss has a lower bound that depends on the DPP. Moreover, for any desired DPP, we derive model parameters that ensure the largest possible efficiency.     

Design-based or Prediction-based Inference? Stratified Random vs Stratified Balanced Sampling

Early survey statisticians faced a puzzling choice between randomized sampling and purposive selection but, by the early 1950s, Neyman's design-based or randomization approach had become generally accepted as standard. It remained virtually unchallenged until the early 1970s, when Royall and his co-authors produced an alternative approach based on statistical modelling. This revived the old idea of purposive selection, under the new name of “balanced sampling”. Suppose that the sampling strategy to be used for a particular survey is required to involve both a stratified sampling design and the classical ratio estimator, but that, within each stratum, a choice is allowed between simple random sampling and simple balanced sampling; then which should the survey statistician choose? The balanced sampling strategy appears preferable in terms of robustness and efficiency, but the randomized design has certain countervailing advantages. These include the simplicity of the selection process and an established public acceptance that randomization is “fair”. It transpires that nearly all the advantages of both schemes can be secured if simple random samples are selected within each stratum and a generalized regression estimator is used instead of the classical ratio estimator.     

测边后方交会的直接计算方法

在图根控制测量中,交会定点是一种常用、简单的加密平面控制点的方法,有必要探讨在待定点上观测三条边长情况下的交会定点的直接计算问题。     

A mixed-mode sensitive research on cannabis use and sexual addiction: improving self-reporting by means of indirect questioning techniques

In this article, we describe the methods employed and the results obtained from a mixed-mode “sensitive research” conducted in Spain to estimate certain aspects concerning patterns of cannabis consumption and sexual addiction among university students. Three different data-collection methods are considered and compared: direct questioning, randomized response technique and item sum technique. It is shown that posing direct questions to obtain sensitive data produces significantly lower estimates of the surveyed characteristics than do indirect questioning methods. From the analysis, it emerges that male students seem to be more affected by sex addiction than female students while for cannabis consumption there is no evidence of a predominant gender effect.     

Post‐Stratification Weighting in Organizational Surveys: A Cross‐Disciplinary Tutorial

Post‐stratification weighting is a technique used in public opinion polling to minimize discrepancies between population parameters and realized sample characteristics. The current paper provides a weighting tutorial to organizational surveyors who may otherwise be unfamiliar with the rationale behind the practice as well as “when and how to do” such weighting. The primary reasons to weight include: [1] reducing the effect of frame, sampling, and nonresponse bias in point estimates, and, relatedly, (2) correcting for aggregation error resulting from over‐ and underrepresentation of constituent groups. We briefly compare and contrast traditions within public opinion and organizational polling contexts and present a hybrid taxonomy of sampling procedures that organizational surveyors may find useful in situating their survey efforts within a methodological framework. Next, we extend the existing HRM literature focused on survey nonresponse to a broader lens concerned with population misrepresentation. It is from this broadened methodological framework that we introduce the practice of weighting as a remedial strategy for misrepresentation. We then provide sample weighting algorithms and standard error corrections that can be applied to organizational survey data and make our data and procedures available to individuals who may wish to use our examples as they learn “how to weight.” © 2018 Wiley ­Periodicals, Inc.     

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.     

Mixture of Truthful–Untruthful Responses in Public Surveys

When sensitive issues are surveyed, collecting truthful data and obtaining reliable estimates of population parameters is a persistent problem in many fields of applied research mostly in sociological, economic, demographic, ecological and medical studies. In this context, and moving from the so‐called negative survey, we consider the problem of estimating the proportion of population units belonging to the categories of a sensitive variable when collected data are affected by measurement errors produced by untruthful responses. An extension of the negative survey approach is proposed herein in order to allow respondents to release a true response. The proposal rests on modelling the released data with a mixture of truthful and untruthful responses that allows researchers to obtain an estimate of the proportions as well as the probability of receiving the true response by implementing the EM‐algorithm. We describe the estimation procedure and carry out a simulation study to assess the performance of the EM estimates vis‐à‐vis certain benchmark values and the estimates obtained under the traditional data‐collection approach based on direct questioning that ignores the presence of misreporting due to untruthful responding. Simulation findings provide evidence on the accuracy of the estimates and permit us to appreciate the improvements that our approach can produce in public surveys, particularly in election opinion polls, when the hidden vote problem is present.     

Probing: A dangerous practice in social surveys?

It is widely accepted among survey researchers that the use of probes by their interviewers can lead to more intelligible, more complete, and more easily coded answers from respondents. Yet it is not hard to find examples of the use of probes in the survey research literature that have failed to produce demonstrably better data. Since the poor codability of respondents' answers is the product of a number of factors, merely training interviewers to be more skilful in their use of probes is unlikely to significantly improve the quality of survey data. If probes are to be used, they should be both standardized and used systematically. It would be better, however, to try to eliminate the need for interviewers to have to use probes. Two positive steps the researcher can take in this direction are: to define key terms properly, and to specify the response frameworks that respondents should adopt when formulating replies to particular questions.     

Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

In survey sampling, auxiliary information on the population is often available. The aim of this paper is to develop a method which allows one to take into account such auxiliary information at the estimation stage by means of conditional bias adjustment. The basic idea is to attempt to construct a conditionally unbiased estimator. Four estimators that have a small conditional bias with respect to a statistic are proposed. It is shown that many of the estimators used in the literature in the case of simple random sampling can be obtained by using this estimation principle. The problem of simple random sampling with replacement, poststratification, and adjustment of a 2 x 2 dimensional contingency table to marginal totals are discussed in the conditional framework. Finally it is shown that the regression estimator can be viewed as an approximation of an application of the conditional principle.     

Microsimulation of Business Performance

Microsimulation of business performance based on sample survey data is a relatively underdeveloped field, but its application in government economic policy formulation is potentially great since it can be used to measure the distributional effects of change rather than just average change. Techniques which account for the dynamic response of businesses to macro level price expectations have recently been developed (Kokic et al. , 1993). These allow individual level business performance to be forecast from sample survey data. In this paper we outline a general methodology for combining these forecasting techniques with Monte Carlo simulation in order to produce a microsimulation of business performance that accurately captures the true distributional characteristics of the underling survey data. Applying this methodology to Australian farm survey data, we show that these methods may be used to forecast the distribution of farm business production and performance within arbitrary subdomains of the surveyed population conditional on a given set of expected commodity price outcomes. The microsimulations reflect both the uncertainty due to climatic variation from one year to the next, which in the Australian context depends largely on geographic location, as well as the uncertainty of commodity prices.     

Endogenous technology and sectoral productivity: Chile 1962–1982

The choice of sectoral productivity in Chile is studied within the choice of technique approach. The choice of production techniques is an economic problem in that the techniques implemented at any time reflect the prevailing economic environment, as well as its history. Incorporating this choice in the analysis adds another channel through which market conditions can influence productivity while neglecting this simple fact leads to a distorted view of the production process. This view of production is applied here to present an econometric framework for estimating sectoral production functions. The derived function has the form of a Cobb-Douglas function, but its coefficients are allowed to vary in response to the economic environment and to factor utilization. The results show the important effect that macro, external, and institutional shocks have on the level and cyclical behavior of productivity.The editor of this paper was Jaime de Melo.     

Panel design effects on response rates and response quality

To understand changes in individuals' opinions and attitudes, it would be best to collect data through panels. Such panels, however, often cause irritation among respondents, resulting in low response rates and low response quality. We address whether this problem can be alleviated by designing a panel survey in an alternative way. For this purpose, we perform two field studies where we measure the effects of several panel design characteristics on response rates and response quality. These characteristics include the number of waves and the time between subsequent waves, which may be either fixed or random. Our findings suggest that response rates and response quality can be improved significantly by surveying at random time intervals. It is then crucial that panel members are not informed about the dates they will be surveyed, because in this case, respondents are less likely to develop expectations as to when they will be surveyed again. The methodology we put forward can be used to improve the efficiency of a panel study by carefully calibrating the studies' panel design parameters.     

Alternative Indicators for the Risk of Non‐response Bias: A Simulation Study

The growth of non‐response rates for social science surveys has led to increased concern about the risk of non‐response bias. Unfortunately, the non‐response rate is a poor indicator of when non‐response bias is likely to occur. We consider in this paper a set of alternative indicators. A large‐scale simulation study is used to explore how each of these indicators performs in a variety of circumstances. Although, as expected, none of the indicators fully depict the impact of non‐response in survey estimates, we discuss how they can be used when creating a plausible account of the risks for non‐response bias for a survey. We also describe an interesting characteristic of the fraction of missing information that may be helpful in diagnosing not‐missing‐at‐random mechanisms in certain situations.     

Hierarchical Models for the Analysis of Likert Scales in Regression and Item Response Analysis

Appropriate modelling of Likert‐type items should account for the scale level and the specific role of the neutral middle category, which is present in most Likert‐type items that are in common use. Powerful hierarchical models that account for both aspects are proposed. To avoid biased estimates, the models separate the neutral category when modelling the effects of explanatory variables on the outcome. The main model that is propagated uses binary response models as building blocks in a hierarchical way. It has the advantage that it can be easily extended to include response style effects and non‐linear smooth effects of explanatory variables. By simple transformation of the data, available software for binary response variables can be used to fit the model. The proposed hierarchical model can be used to investigate the effects of covariates on single Likert‐type items and also for the analysis of a combination of items. For both cases, estimation tools are provided. The usefulness of the approach is illustrated by applying the methodology to a large data set.     

Using ad hoc measures for response styles: a cautionary note

This research note addresses the challenge of how to optimally measure acquiescence response style (ARS) and extreme response style (ERS). This is of crucial importance in assessing results from studies that have tried to identify antecedents of response styles (such as age, education level, national culture). Using survey data from the Netherlands, a comparison is made between the traditional method and a more recently proposed method of measuring ARS and ERS (i.e., the convergent validity across both methods is assessed). The traditional method is based on an ad hoc set of related items. The alternative method uses a set of randomly sampled items to optimize heterogeneity and representativeness of the items. It is found that the traditional method may lead to response style measures that are suboptimal for estimating levels of ARS and ERS as well as relations of ARS and ERS with other variables (like hypothesized antecedents). Recommendations on how to measure response styles are provided.