Leading Indicators and Spatial Interactions: A Crime Forecasting Model for Proactive Police Deployment

Date of Original Version



Working Paper

Abstract or Description

Based on crime attractor and displacement theories of environmental criminology, we specify a leading indicator model for forecasting serious property and violent crimes. The model, intended for support of tactical deployment of police resources, is at the micro-level scale; namely, one-month-ahead forecasts over a grid system of 104 square grid cells 4,000 feet on a side (with approximately 100 blocks per grid cell). The leading indicators are selected lesser crimes and incivilities entering the model in two ways: 1) as time lags within grid cells and 2) time and space lags averaged over contiguous grid cells of observation grid cells. Our validation case study uses 1.3 million police records including 16 individual crime types from Pittsburgh, Pennsylvania aggregated over the grid system for a 96 month period ending in December 1998. The study uses the rolling-horizon forecast experimental design with forecasts made over the 36 month period ending in December 1998, yielding 3,774 forecast errors per forecast model. We estimated the leading indicator model using both an OLS linear regression model and a nonlinear neural network, plus included a proven univariate, extrapolative forecast method as a benchmark for a Granger causality assessment. The analytical approach to forecast validation is based on decision support requirements of police for crime prevention. Needed is information on large forecasted changes in crime. The leading indicator models have the comparative advantage over extrapolative methods of being able to forecast the largest changes in crime, those due to breaks in crime series data such as step jumps in the forecast period. Expectations for forecast results should be that they yield good if imperfect leads on where to deploy crime analysts, patrols and detectives; for example, if 50 percent of forecasted large changes were “positives,” that would be a success. The end results are that the leading indicator models provide acceptable forecasts and are significantly better than the extrapolative method in three out of four cases, and for the fourth there is a tie but poor forecast performance. The leading indicators find 38 to 54 percent of positives in the three successful cases. The resulting workload for police is quite acceptable, with on the average of 7 large change cases per month with two thirds of such cases being false positives.