A Spatially Correlated Auto-Regressive Model for Count Data with Applications for Modeling Crime

• Activity Number: 475 - SPEED: Predictive Analytics with Social/Behavioral Science Applications: Spatial Modeling, Education Assessment, Population Behavior, and the Use of Multiple Data Sources
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Nicholas Clark* and Philip M Dixon
• Companies: Iowa State University and Iowa State University
• Keywords: Burglaries; Space-Time Correlation; Bayesian; Self-Exciting; Markov

Abstract

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. 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. We apply Bayesian inference for the SPINGARCH process demonstrating its use in modeling the spatio-temporal structure of burglaries in Chicago from 2010-2015 and demonstrate how accounting for spatial correlation changes the conclusion on the existence of repeat victimization.