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.

中文翻译：

---

公共调查中真实与非真实反应的混合

当对敏感问题进行调查时，在许多社会，经济，人口，生态和医学研究的应用研究领域，收集真实数据并获得可靠的人口参数估计是一个长期存在的问题。在这种情况下，从所谓的否定调查出发，我们考虑的问题是，当收集的数据受到不真实的响应产生的测量误差的影响时，估算属于敏感变量类别的人口单位的比例。本文提出了否定调查方法的扩展，以允许受访者发表真实的回答。该建议基于对真实和不真实的响应进行混合而对发布的数据进行建模，这使研究人员可以通过实施EM算法来获得比例的估计以及接收到真实响应的可能性。我们描述了估算程序，并进行了仿真研究，以评估EM估算相对于某些基准值的性能，以及根据传统数据收集方法基于直接质疑而忽略了由于以下原因导致的误报的估算值：不真实的回应。模拟结果为估算的准确性提供了证据，并使我们能够赞赏我们的方法可以在公开调查中产生的改进，尤其是在存在隐藏投票问题的情况下，尤其是在选举民意测验中。