A Spatially Correlated Auto-regressive Model for Count Data
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The statistical modeling of multivariate count data observed on a space-time lattice has generally focused on using a hierarchical modeling approach where space-time correlation structure is placed on a continuous, unobservable, process. The count distribution is then assumed to be conditionally independent given the latent process. However, in many real-world applications, especially in the modeling of criminal or terrorism data, the conditional independence between the count distributions is inappropriate. In the absence of spatial correlation, the Integer Auto-Regressive Conditionally Heteroskedastic (INGARCH) process could be used to capture this data model dependence however this model does not allow for any unexplained spatial correlation in the data. In this manuscript we propose a class of models that extends the INGARCH process to account for small scale spatial variation, which we refer to as a SPINGARCH process. The resulting model allows both data model dependence as well as dependence in a latent structure. We demonstrate how second-order properties can be used to differentiate between models in this class. Finally, we apply Bayesian inference for the SPINGARCH process demonstrating its use in modeling the spatio-temporal structure of burglaries in Chicago from 2010-2015.
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