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The crosswise model is an increasingly popular survey technique to elicitcandid answers from respondents on sensitive questions. Recent studies,however, point out that in the presence of inattentive respondents, theconventional estimator of the prevalence of a sensitive attribute is biasedtoward 0.5. To remedy this problem, we propose a simple design-based biascorrection using an anchor question that has a sensitive item with knownprevalence. We demonstrate that we can easily estimate and correct for the biasarising from inattentive respondents without measuring individual-levelattentiveness. We also offer several useful extensions of our estimator,including a sensitivity analysis for the conventional estimator, a strategy forweighting, a framework for multivariate regressions in which a latent sensitivetrait is used as an outcome or a predictor, and tools for power analysis andparameter selection. Our method can be easily implemented through ouropen-source software, cWise.

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