The Analysis of Criminal Recidivism: A Hierarchical Model-Based Approach for the Analysis of Zero-Inflated, Spatially Correlated recurrent events Data

The life course perspective in criminology has become prominent last years, offering valuable insights into various patterns of criminal offending and pathways. The study of criminal trajectories aims to understand the beginning, persistence and desistence in crime, providing intriguing explanations about these moments in life. Central to this analysis is the identification of patterns in the frequency of criminal victimization and recidivism, along with the factors that contribute to them. Specifically, this work introduces a new class of models that overcome limitations in traditional methods used to analyze criminal recidivism. These models are designed for recurrent events data characterized by excess of zeros and spatial correlation. They extend the Non-Homogeneous Poisson Process, incorporating spatial dependence in the model through random effects, enabling the analysis of associations among individuals within the same spatial stratum. To deal with the excess of zeros in the data, a zero-inflated Poisson mixed model was incorporated. In addition to parametric models following the Power Law process for baseline intensity functions, we propose flexible semi-parametric versions approximating the intensity function using Bernstein Polynomials. The Bayesian approach offers advantages such as incorporating external evidence and modeling specific correlations between random effects and observed data. The performance of these models was evaluated in a simulation study with various scenarios, and we applied them to analyze criminal recidivism data in the Metropolitan Region of Belo Horizonte, Brazil. The results provide a detailed analysis of high-risk areas for recurrent crimes and the behavior of recidivism rates over time. This research significantly enhances our understanding of criminal trajectories, paving the way for more effective strategies in combating criminal recidivism.