Regressão Bessel bayesiana com efeito espaço-temporal para dados contínuos limitados

Abstract

This work contributed to a Bayesian implementation of the Bessel regression model for limited data with a spatiotemporal correlation structure and provided comprehensive comparisons among different models. We introduced three models - M1, M2, and M3 - primarily differing in the inclusion of covariates and temporal effects. M1 can be considered a simplification of M2, where we summarize covariates with measurements over time (M2 uses all measurements from distinct time points). Both M1 and M2 incorporate random effects (spatial and temporal) additively in the linear predictor explaining the mean. On the other hand, in M3, only the spatial effect is additive, and the temporal effect is introduced through time-varying coefficients. We conducted simulations in various misspecification scenarios of the effects and compared the Relative Biases (RBs) of the estimates of the main parameters. In cases where there is no information about the data structure, M2 proved to be the most suitable as it showed adjustments with smaller RBs in misspecification situations. However, when the analyst knows the form of the data-generating model, using the well-specified model is always the best option, as we obtain more reliable estimates with RBs closer to zero. In the real-world application, we used an electoral democracy index as the response variable and five socioeconomic, environmental, and geographical indices as covariates explaining the mean of the Bessel model. We applied all three models and analyzed the posterior estimates. Among the three proposals, M2 with three covariates yielded the most interesting results. The variables selected in this adjustment were “Annual Air Pollution Index”, “Waste Treatment Index” and “Female Prevalence”. The first exhibited a negative relationship with the response variable, while the latter two showed a positive relationship, which aligns with expectations. Additionally, we observed a decreasing pattern in the values of the temporal effect from 2013 onwards, which may be related to geopolitical instabilities that occurred during that period.