🧭 Problem:
The crosswise model is a popular survey technique for eliciting truthful answers to sensitive questions, but inattentive respondents cause the conventional prevalence estimator to be biased toward 0.5. This bias threatens validity when respondents answer carelessly and cannot be identified individually.
🛠️ Proposed Fix:
A simple, design-based bias correction is introduced that uses an anchor question containing a sensitive item with known prevalence. This anchor allows estimation and correction of the bias attributable to inattentive respondents without measuring attentiveness at the individual level.
🔎 How the Correction Works:
- Embed an anchor question with a sensitive item whose true prevalence is known.
- Use the observed responses to estimate the aggregate bias produced by inattentive respondents.
- Adjust the conventional crosswise estimator using that estimated bias to recover corrected prevalence estimates.
📈 Key Findings:
- The conventional estimator is shown to be biased toward 0.5 in the presence of inattentiveness.
- The anchor-based, design correction reliably estimates and removes that bias at the aggregate level.
- Individual-level attentiveness measures are not required for effective correction.
🧩 Extensions and Practical Tools:
- A sensitivity analysis for the conventional estimator to assess robustness when no anchor is available.
- A weighting strategy to incorporate sample design or poststratification adjustments.
- A framework for multivariate regressions that treats the latent sensitive trait as either an outcome or a predictor.
- Tools for power analysis and parameter selection tailored to crosswise designs.
💻 Implementation:
The method is implemented in the open-source software cWise, enabling easy application of the bias correction, extensions, and power tools in empirical work.
⚖️ Why It Matters:
This correction preserves the advantages of the crosswise model for sensitive questions while addressing a common source of bias, making prevalence estimates and downstream regression analyses more reliable in the presence of inattentive respondents.
