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.