A Bias-Corrected Estimator for the Crosswise Model with Inattentive Respondents

The crosswise model is an increasingly popular survey technique to elicit candid answers from respondents on sensitive questions. Recent studies, however, point out that in the presence of inattentive respondents, the conventional estimator of the prevalence of a sensitive attribute is biased toward 0.5. To remedy this problem, we propose a simple design-based bias correction using an anchor question that has a sensitive item with known prevalence. We demonstrate that we can easily estimate and correct for the bias arising from inattentive respondents without measuring individual-level attentiveness. We also offer several useful extensions of our estimator, including a sensitivity analysis for the conventional estimator, a strategy for weighting, a framework for multivariate regressions in which a latent sensitive trait is used as an outcome or a predictor, and tools for power analysis and parameter selection. Our method can be easily implemented through our open-source software cWise.