A Spatiotemporal Bayesian Hierarchical Approach to Investigating Patterns of Confidence in the Police at the Neighborhood Level

Abstract

Public confidence in the police is crucial to effective policing. Improving understanding of public confidence at the local level will better enable the police to conduct proactive confidence interventions to meet the concerns of local communities. Conventional approaches do not consider that public confidence varies across geographic space as well as in time. Neighborhood level approaches to modeling public confidence in the police are hampered by the small number problem and the resulting instability in the estimates and uncertainty in the results. This research illustrates a spatiotemporal Bayesian approach for estimating and forecasting public confidence at the neighborhood level and we use it to examine trends in public confidence in the police in London, UK, for Q2 2006 to Q3 2013. Our approach overcomes the limitations of the small number problem and specifically, we investigate the effect of the spatiotemporal representation structure chosen on the estimates of public confidence produced. We then investigate the use of the model for forecasting by producing one-step ahead forecasts of the final third of the time series. The results are compared with the forecasts from traditional time-series forecasting methods like na€ ıve, exponential smoothing, ARIMA, STARIMA, and others. A model with spatially structured and unstructured random effects as well as a normally distributed spatiotemporal interaction term was the most parsimonious and produced the most realistic estimates. It also provided the best forecasts at the London-wide, Borough, and neighborhood level.

Spatiotemporal Modeling of Correlated Small‐Area Outcomes: Analyzing the Shared and Type‐Specific Patterns of Crime and Disorder

“…With a temporal adjacency matrix, the ICAR prior distribution has also been applied to model nonlinear time trends (Richardson et al ; Quick et al ). Past studies applying Bayesian spatiotemporal models to small‐area crime data have analyzed violent crime and property crime over two years (Law et al ; ), burglary over 4‐ and 8‐year time periods (Li et al ; ), and police confidence over 36 quarters (Williams et al ). Quick et al () use a Bayesian multivariate model to analyze burglary, robbery, vehicle crime, and violent crime, and identify two crime‐general spatial patterns shared amongst all crimes and the three theft‐related crimes.…”

Applying the Spatial EBLUP to Place-Based Policing. Simulation Study and Application to Confidence in Police Work

“…Taylor (2013) made use of multilevel models to produce synthetic estimates of perceived antisocial behaviour in England and Wales. Williams et al (2019) introduced the spatially correlated random area effects and produced neighborhood estimates of public confidence in policing from a spatiotemporal Bayesian approach. Wheeler et al (2017) made use of spatial models to produce synthetic estimates of attitudes towards the police.…”

“…In this research, we consider the Restricted Maximum Likelihood estimator, which takes into account for the loss in degrees of freedom derived from estimating β, while other estimators, such as the Maximum Likelihood estimator, do not (Rao and Molina 2015). The assumption of normality of the random effects is reasonable in those cases in which area-level direct estimates are normally distributed, as tends to be the case in criminological studies looking into the confidence in police work (Williams et al 2019), emotions about crime (Whitworth 2012) and rates of some crime types at large spatial scales (Fay and Diallo 2012). However, such assumption may be considered invalid in those cases in which the normality of direct estimates is not met.…”

“…Moreover, government inspections into police forces assess not only their effectiveness in reducing crime, but also they expect the police to develop programs to enhance its legitimacy and public confidence in those geographical areas where public cooperation with police services is lower (HMICFRS 2017). The confidence in police work is also distributed at micro places (Williams et al 2019), and thus should be taken into account to design place-based policing strategies.…”

“…This is one of the first papers that evaluates and applies these methods in policing research and practice. Confidence in police work tends to show high levels of spatial clustering (Jackson et al 2013;Williams et al 2019), which can be taken into account in SAE models to increase the estimates' precision. In SAE, the use of spatially correlated random area effects is increasingly in use (Chandra et al 2007;Petrucci and Salvati 2006;Pratesi and Salvati 2008;Salvati et al 2014).…”