Modelling 'crime-proneness'. A comparison of models for repeated count outcomes

In the criminal career literature, the individual-level age-crime relationship is commonly modelled using generalized linear mixed models, where between-individual heterogeneity is then handled through specifying random effect(s) with some distribution. It is common to specify either a normal or discrete distribution for the random effects. However, there are also other options, and the choice of specification might have substantial effect on the results. In this article, we compare how various methods perform on Norwegian longitudinal data on registered crimes. We also present an approach that might be new to criminologists: the Poisson-gamma regression model. This model is interpretable, parsimonious, and quick to compute. For our data, the distributional assumptions have not dramatic effect on substantive interpretation. In criminology, the mixture distribution is also of theoretical interest by its own right, and we conclude that a gamma distribution is reasonable. We emphasize the importance of comparing multiple methods in any setting where the distributional assumptions are uncertain.