Bias-Corrected Crosswise Estimators for Sensitive Inquiries
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The crosswise model is an increasingly popular survey technique to elicit candid answers from respondents on sensitive questions. We demonstrate, however, that the conventional crosswise estimator for the population prevalence of sensitive attributes is biased toward 0.5 in the presence of inattentive respondents who randomly choose their answers under this design. We propose a simple design-based bias correction procedure and show that our bias-corrected estimator can be easily implemented without measuring individual-level attentiveness. We also offer several useful extensions of our bias correction, including a sensitivity analysis for conventional crosswise estimates, a strategy for weighting, and a framework for multivariate regressions in which a latent sensitive trait is used as an outcome or a predictor. We illustrate our methodology by simulation studies and empirical examples and provide a practical guide for designing surveys to enable our proposed bias correction. Our method can be easily implemented through our open-source software,cWise.
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