Modelos de regressão espacial para dados de contagem com inflação de zeros

Abstract

Spatial regression models are used to investigate the relationship between variables of interest and explanatory factors when there is geographic dependence among the units of analysis. Among the most well-established approaches in this context are conditional autoregressive (CAR) models, particularly the parameterizations proposed by Besag, York and Mollié (BYM), BYM2 and Leroux, which allow the incorporation of structured and unstructured spatial effects. In applications involving rare events, the presence of zero inflation in the response variable is frequent, which motivates the use of Zero-Inflated Poisson (ZIP) models. In this study, specifications of Bayesian spatial regression models were compared, combining CAR structures (BYM, BYM2 and Leroux) with Poisson and ZIP distributions, using the goodness-of-fit criteria DIC, WAIC and LMPL. The methodology was applied to two case studies. The first analyzed the number of confirmed cases of leptospirosis in the 853 municipalities of the state of Minas Gerais, from 2022 to 2024, characterized by high zero inflation (80.89%) and moderate positive spatial autocorrelation. The second evaluated fire hotspots in municipalities of the Brazilian Northeast in March 2025, data marked by strong spatial heterogeneity and excess zeros (37.01%). The results indicated the presence of spatial dependence in both contexts, with superior performance of spatial models compared to unstructured alternatives. In the case of leptospirosis, the CAR BYM ZIP model showed the best fit, highlighting the importance of simultaneously accommodating the spatial structure and the zero-generating process. For fire hotspots, the CAR BYM2 ZIP models showed greater stability and better performance, highlighting the suitability of more parsimonious parameterizations in complex environmental scenarios. Transversally, it was observed that there is no universally superior choice among BYM, BYM2 and Leroux, with model performance depending on the intensity of spatial autocorrelation, the proportion of structural zeros and the residual variability of the data. It is concluded that the combination of hierarchical spatial models and zero-inflated distributions constitutes a robust strategy for modeling rare events in different empirical contexts. The findings contribute methodologically to the critical comparison of CAR parameterizations and, from an applied perspective, provide support for more stable and informative epidemiological and environmental analyses at the territorial level.