Considerations for developing predictive spatial models of crime and new methods for measuring their accuracy

Abstract

A literature review of the important trends in predictive crime modeling and the existing measures of accuracy was undertaken. It highlighted the need for a robust, comprehensive and independent evaluation and the need to include complementary measures for a more complete assessment. We develop a new measure called the penalized predictive accuracy index (PPAI), propose the use of the expected utility function to combine multiple measures and the use of the average logarithmic score, which measures accuracy differently than existing measures. The measures are illustrated using hypothetical examples. We illustrate how PPAI could identify the best model for a given problem, as well as how the expected utility measure can be used to combine different measures in a way that is the most appropriate for the problem at hand. It is important to develop measures that empower the practitioner with the ability to input the choices and preferences that are most appropriate for the problem at hand and to combine multiple measures. The measures proposed here go some way towards providing this ability. Further development along these lines is needed.