The Extended Crosswise Model Adjusted for Random Answering

TL;DR

This paper introduces two new methods to detect and correct for random answering in the Extended Crosswise Model, enhancing the accuracy of sensitive behavior prevalence estimates.

Contribution

It proposes novel techniques using control statements and response time analysis to estimate and adjust for random answering in the model.

Findings

Methods successfully estimated the proportion of random respondents.

Corrected doping prevalence estimates among elite athletes.

Improved reliability of sensitive behavior surveys.

Abstract

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.