Abstract
This research investigates spatio-temporal patterns of police calls-for-service in the Region of Waterloo, Canada, at a fine spatial and temporal resolution. Modeling was implemented via Bayesian Integrated Nested Laplace Approximation (INLA). Temporal patterns for two-hour time periods, spatial patterns at the small-area scale, and space-time interaction (i.e., unusual departures from overall spatial and temporal patterns) were estimated. Temporally, calls-for-service were found to be lowest in the early morning (02:00–03:59) and highest in the evening (20:00–21:59), while high levels of calls-for-service were spatially located in central business areas and in areas characterized by major roadways, universities, and shopping centres. Space-time interaction was observed to be geographically dispersed during daytime hours but concentrated in central business areas during evening hours. Interpreted through the routine activity theory, results are discussed with respect to law enforcement resource demand and allocation, and the advantages of modeling spatio-temporal datasets with Bayesian INLA methods are highlighted.
Highlights
In law enforcement, the implementation of computer-aided dispatch systems that automatically record location- and time-specific information for police calls-for-service has facilitated the storage, retrieval, and analysis of large volumes of spatio-temporal data [1,2,3,4,5]
Applied to police resource allocation, dispatch staffing should peak at these two time periods, higher levels of police units capable of responding to motor vehicle collisions should be staffed during 10:00–11:59 and higher levels of bylaw enforcement should be staffed during 20:00–21:59
This research applied a Bayesian spatio-temporal modeling approach implemented via Integrated Nested Laplace Approximation (INLA) to identify spatial, temporal, and space–time patterns of calls-for-service for two-hour time periods at the small-area level
Summary
The implementation of computer-aided dispatch systems that automatically record location- and time-specific information for police calls-for-service has facilitated the storage, retrieval, and analysis of large volumes of spatio-temporal data [1,2,3,4,5]. While useful for identifying overall levels of space-time clustering for a dataset, testing-based methods do not identify overall spatial and temporal patterns (i.e., for the study region) and do not provide risk estimates for observations not identified as hotspots. Model-based spatio-temporal methods for small-area data decompose observed space-time data into overall spatial and overall temporal patterns, as well as space-time interaction. Estimates of these components are not feasible by comparing maps or count or rate data, when the number of space-time units is large. Bayesian methods combine observed data (i.e., space-time incident counts) and prior information (i.e., spatial and temporal structures) to estimate posterior probability distributions of model parameters, including space-time interaction [28]. We reflect on the use of Bayesian spatio-temporal models and INLA to model spatio-temporal datasets
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