Violence against women in Italy: correcting underreported data

Violence Against Women (VAW) is a pervasive and often underreported phenomenon, posing significant challenges for measurement and policy intervention. In Italy, the lack of recent and regularly updated ad hoc survey data has motivated our interest in official registers as an alternative source of geographically referenced information for estimating violence rates; however, these data are subject to significant underreporting. This study analyses VAW across Italian provinces using police registry data from 2020 within a hierarchical Bayesian Poisson regression framework. We adopt a Pogit model that accounts for the reporting mechanism, enabling joint inference on both the incidence of violence and the probability of reporting at the provincial level, incorporating socioeconomic and spatial covariates. To evaluate the robustness of the proposed approach, we conduct a simulation study assessing the sensitivity of posterior inferences to prior specification and covariate choice. The results indicate that the model accurately recovers both model parameters and true counts, even when only proxy covariates are available to model underreporting. Overall, the results underscore the importance of covariate quality and prior specification in improving inference and informing policies, particularly in settings where administrative data are biased or incomplete.