Likelihood‐Based Inference and Prediction in Spatio‐Temporal Panel Count Models for Urban Crimes

PRELIMINARY DRAFT We discuss maximum likelihood (ML) analysis for panel count data models, in which the observed counts are linked via a measurement density to a latent Gaussian process with spatial as well as temporal dynamics and random effects. For likelihood evaluation requiring high-dimensional integration we rely upon Efficient Importance Sampling (EIS). The algorithm we develop extends existing EIS implementations by constructing importance sampling densities, which closely approximate the nontrivial spatio-temporal correlation structure under dynamic spatial panel models. In order to make this high-dimensional approximation computationally feasible, our EIS implementation exploits the typical sparsity of spatial precision matrices in such a way that all the high-dimensional matrix operations it requires can be performed using computationally fast sparse matrix functions. We use the proposed sparse EIS-ML approach for an extensive empirical study analyzing the socio-demographic determinants and the space-time dynamics of urban crime in Pittsburgh, USA, between 2008 and 2013 for a panel of monthly crime rates at census-tract level.(This abstract was borrowed from another version of this item.)