Spatial eigenvector filtering for spatiotemporal crime mapping and spatial crime analysis

Spatial and spatiotemporal analyses are exceedingly relevant to determine criminogenic factors. The estimation of Poisson
and negative binomial models (NBM) is complicated by spatial autocorrelation. Therefore, first, eigenvector spatial filtering
(ESF) is introduced as a method for spatiotemporal mapping to uncover time-invariant crime patterns. Second, it is
demonstrated how ESF is effectively used in criminology to invalidate model misspecification, i.e., residual spatial
autocorrelation, using a nonviolent crime dataset for the metropolitan area of Houston, Texas, over the period 2005–
2010. The results suggest that local and regional geography significantly contributes to the explanation of crime patterns.
Furthermore, common space-time eigenvectors selected on an annual basis indicate striking spatiotemporal patterns
persisting over time. The findings about the driving forces behind Houston’s crime show that linear and nonlinear, spatially
filtered, NBMs successfully absorb latent autocorrelation and, therefore, prevent parameter estimation bias. The consideration
of a spatial filter also increases the explanatory power of the regressions. It is concluded that ESF can be highly
recommended for the integration in spatial and spatiotemporal modeling toolboxes of law enforcement agencies.