Similarity measures for behavioural crime linkage with sparse and imperfect data

Behavioural crime linkage compares pairs of crimes with a similarity measure, usually Jaccard, and evaluates it with the area under the ROC curve (AUC), but it is unknown when and why one measure outperforms another. Using 27,460 simulated datasets (not counting versions with errors), we compared Jaccard, simple matching, Goodall3 (which adds shared presences and, with a weight that increases with the frequency of the behaviour, shared absences), other measures and trained models, varying the behaviours, offender consistency, non-serial crimes, recording quality and generator assumptions, and applied them to Godwin's (1998) real data. In Study 1, Goodall3 outperformed Jaccard on AUC in 203 of 300 conditions, was slightly better in 20 and equivalent in 77, never worse; in the real data its advantage was small. That advantage is associated mainly with its form, which does not divide by recorded behaviours, and over half of it with crimes lacking recorded behaviours; frequency weighting contributed mainly to the AUPRC (area under the precision–recall curve). On AUPRC it was better in most conditions, but not in those most similar to a police system, where an index that adds presences and a trained model were more precise; its advantage was nearly halved with correlated behaviours. Without training, it reached an AUC comparable to a Bayesian model trained on five datasets. Non-serial crimes barely changed the AUC but sharply reduced predictive value. Goodall3 is a promising reference measure alongside Jaccard, not a universally superior one, and evaluations should include precision and recording quality.