Abstract
Socioeconomically disadvantaged populations are often disproportionately subjected to over policing. While sometimes well intended, other times over policing is due to a belief that a response to crime must be swift in order to deter possible repeat actors. However, crime inspired by the action of another criminal is not the only reason why these events may be clustered in space and time. A competing theory states that spatio-temporal clustering occurs due to underlying socio-economic conditions rather than inspired actors. In quantitative criminology, repeat victimization attributed to copy-cat actors is often modeled through the use of a self-exciting, or Hawkes, process. This process is often assumed to exist prior to data analysis and alternative processes are rarely considered. In this manuscript, we will discuss how model selection, in particular model selection between a log Gaussian Cox process and a Hawkes process, is both a necessary as well as difficult step in statistical modeling of crime. We will provide a few techniques to conduct model selection between these processes and conclude, with a warning for researchers in this area, that sometimes these processes cannot be disentangled. In these instances, we suggest that modelers explicitly mention that their models rely on one theory of repeat victimization and that alternative theories may exist that lead to other forms of policing and may impact their interpretation of the root cause of why crime is spreading in space and time.