Bayesian Quantile Regression for Misclassified Binary Data with an Application to Spousal Violence Reporting
Survey responses on socially undesirable behaviors, such as self-reported spousal violence, are often subject to underreporting due to social stigma, fear of retaliation, and other reporting pressures. When such data are analyzed using standard econometric models that focus on conditional means, such as probit and logit models, the resulting estimates are likely to be biased and can obscure heterogeneity in covariate effects. To address these challenges, we propose a Bayesian binary quantile regression framework that accounts for misclassification and provides quantile-specific effects for the latent true response. The framework incorporates false-negative and false-positive probabilities to capture reporting errors and employs a novel partially collapsed Gibbs sampler for estimation. We also discuss the computation of covariate effects and marginal likelihood for Bayesian model comparison. Simulation studies under various settings (prior effective sample size, misclassification rates, and prior distribution) show that accounting for misclassification improves inference across quantiles relative to models that ignore reporting errors. We apply the framework to women's self-reported spousal violence and find that underreporting of spousal violence exceeds overreporting across quantiles, while model comparisons using marginal likelihood generally favor the quantile model with misclassification and yield different conclusions about the determinants of reported violence.