Correlates of homicide: new space/time interaction tests for spatiotemporal point processes

Statistical inference on spatiotemporal data often proceeds by focusing on the temporal aspect of the data, ignoring space, or the spatial aspect, ignoring time. In this paper, we explicitly focus on the interaction between space and time. Using a geocoded, time-stamped dataset from Chicago of almost 9 millions calls to 911 between 2007 and 2010, we ask whether any of these call types are associated with shootings or homicides. Standard correlation techniques do not produce meaningful results in the spatiotemporal setting because of two confounds: purely spatial e ff ects (i.e. “bad” neighborhoods) and purely temporal e ff ects (i.e. more crimes in the summer) could introduce spurious correlations. To address this issue, a handful of statistical tests for space-time interaction have been proposed, which explicitly control for separable spatial and temporal dependencies. Yet these classical tests each have limitations. We propose a new test for space-time interaction, using a Mercer kernel-based statistic for measuring the distance between probability distributions. We compare our new test to existing tests on simulated and real data, where it performs comparably to or better than the classical tests. For the application we consider, we find a number of interesting and significant space-time interactions between 911 call types and shootings / homicides.

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