Shewhart-Type Charts for Masked Data: A Strategy for Handling the Privacy Issue

Data privacy is a serious issue and therefore needs our attention. In this study, we propose masking through randomized response techniques (RRTs) to ensure the privacy and thus to avoid falsification. We assume that the process characteristic is of sensitive nature, and due to privacy issue, the actual measurements cannot be shared with the monitoring team. In such situations, the producer is very likely to falsify the measurements. Consequently, the usual control charting techniques will mislead about the process status. We discuss different data masking strategies to be used with Shewhart-type control charts. The usual Shewhart-type control chart appears to be a subchart of the proposed charts. Average run length (ARL) is used as a performance measure of the study proposals. We have evaluated the performance of the proposed charts for different shift sizes and under different intensities of masking. We have also carried out a comparative analysis for various models under varying sensitivity parameters. We have also compared the performance of the proposals with the traditional Shewhart chart. It is observed that the B-L control chart under the RRT model performs better for smaller shifts and for larger shift sizes, the G-B chart under an unrelated question model tperforms better. A real-life application of the study proposal is also considered where monitoring of thickness of paint on refrigerators is of interest.

Cheater Detection Using the Unrelated Question Model

Randomized response techniques (RRTs) are useful survey tools for estimating the prevalence of sensitive issues, such as the prevalence of doping in elite sports. One type of RRT, the unrelated question model (UQM), has become widely used because of its psychological acceptability for study participants and its favorable statistical properties. One drawback of this model, however, is that it does not allow for detecting cheaters—individuals who disobey the survey instructions and instead give self-protecting responses. In this article, we present refined versions of the UQM designed to detect the prevalence of cheating responses. We provide explicit formulas to calculate the parameters of these refined UQM versions and show how the empirical adequacy of these versions can be tested. The Appendices contain R-code for all necessary calculations.

Generalized Linear Mixed Models for Randomized Responses

Response bias (nonresponse and social desirability bias) is one of the main concerns when asking sensitive questions about behavior and attitudes. Self-reports on sensitive issues as in health research (e.g., drug and alcohol abuse), and social and behavioral sciences (e.g., attitudes against refugees, academic cheating) can be expected to be subject to considerable misreporting. To diminish misreporting on self-reports, indirect questioning techniques have been proposed such as the randomized response techniques. The randomized response techniques avoid a direct link between individual’s response and the sensitive question, thereby protecting the individual’s privacy. Next to the development of the innovative data collection methods, methodological advances have been made to enable a multivariate analysis to relate responses to sensitive questions to other variables. It is shown that the developments can be represented by a general response probability model (including all common designs) by extending it to a generalized linear model (GLM) or a generalized linear mixed model (GLMM). The general methodology is based on modifying common link functions to relate a linear predictor to the randomized response. This approach makes it possible to use existing software for GLMs and GLMMs to model randomized response data. The R-package GLMMRR makes the advanced methodology available to applied researchers. The extended models and software will seriously improve the application of the randomized response methodology. Three empirical examples are given to illustrate the methods.