The Extended Crosswise Model is a popular randomized response design that employs a sensitive and a randomized innocuous statement, and asks respondents if one of these statements is true, or that none or both are true. The model has a degree of freedom to test for response biases, but is unable to detect random answering. In this paper, we propose two new methods to indirectly estimate and correct for random answering. One method uses a non-sensitive control statement and a quasi-randomized innocuous statement to which both answers are known to estimate the proportion of random respondents. The other method assigns less weight in the estimation procedure to respondents who complete the survey in an unrealistically short time. For four surveys among elite athletes, we use these methods to correct the prevalence estimates of doping use for random answering.

翻译：扩展交叉模型是一种流行的随机化应答设计，它采用一个敏感陈述和一个随机化非敏感陈述，并询问受访者其中一个陈述是否为真，或者两者皆非真或两者皆真。该模型具有检验应答偏差的自由度，但无法检测随机应答。本文提出了两种间接估计并校正随机应答的新方法。一种方法使用一个非敏感控制陈述和一个准随机化非敏感陈述（两者的答案已知）来估计随机应答者的比例。另一种方法在估计过程中对在极短时间内完成调查的受访者赋予较低权重。针对精英运动员的四项调查，我们使用这些方法校正了兴奋剂使用流行率估计中的随机应答影响。