Modeling Misclassification in Spousal Violence Reporting: Evidence from Bayesian Quantile Regression

TL;DR

This paper introduces a Bayesian quantile regression method that explicitly models misclassification in binary outcomes, improving inference accuracy in sensitive survey data such as spousal violence reports.

Contribution

It develops a novel Bayesian quantile regression framework with a MCMC algorithm to handle misclassified binary data, addressing biases from underreporting.

Findings

Underreporting exceeds overreporting in the data

Accounting for misclassification alters substantive conclusions

The method outperforms models ignoring misclassification

Abstract

Quantile regression extends regression analysis beyond the conditional mean, providing a richer characterization of covariate effects across the outcome distribution. For sensitive binary outcomes, however, misclassification due to underreporting can substantially bias inference. We propose a Bayesian quantile regression framework for misclassified binary outcomes that introduces a latent true response and explicitly models false negative and false positive reporting errors. Estimation is performed through a novel Markov chain Monte Carlo (MCMC) algorithm. Simulation studies under varying prior specifications and misclassification rates demonstrate improved performance over models that ignore misclassification. We apply the method to self-reported spousal violence data, examining associations with employment status and household wealth while adjusting for socio-demographic factors. The results indicate that underreporting exceeds overreporting across quantiles and that accounting for misclassification can change substantive conclusions.