Under-reported data: a simulation study about parameter sensitivity

The problem of underreported data is a frequently analyzed issue in statistics and concerns a wide range of phenomena, from medical to social aspects, and more. Traditional statistical models often fail to adequately address under-reporting biases, leading to systematic underestimation of true incidence rates. In this study, we analyze one of the main models developed within a hierarchical Bayesian framework to address and correct underreported spatio-temporal count data: the Pogit model. The proposed model assumes a latent Poisson distribution for true incidence counts and a Binomial observation mechanism to account for misreporting, incorporating spatially structured and unstructured random effects. To mitigate identifiability issues, we employ informative priors on the intercept of the logit model for the reporting probability. Through a simulation study, we analyze the sensitivity of parameter estimates to prior misspecification and evaluate the impact of using proxy covariates with varying degrees of correlation to the true reporting mechanism.