Crime Mapping and Spatial Data Analysis using R

This chapter has introduced some of the issues associated with spatial regression. We have deliberately avoided mathematical detail and focused instead on providing a general and more superficial introduction of some of the issues associated with fitting, choosing, and interpreting basic spatial regression models in R. We have also favoured the kind of models that have been previously discussed in the criminological literature, those relying on the frequentist tradition, use of maximum likelihood, simultaneous autoregressive models, and the incorporation of the spatial structure through a neighbourhood matrix. These are not the only ways of fitting spatial regression, though. The functions of spatialreg, for example, allow for newer generalised method of moments (GMM) estimators. On the other hand, other scientific fields have emphasised conditional autoregressive models (see [212] for the difference between CAR and SAR), and there is too a greater reliance, for example in spatial epidemiology, on Bayesian approaches. Equally, we have only focused on cross-sectional models, without any panel or spatio-temporal dimension to them. As Ralph Sockman was attributed to saying, "the larger the island of knowledge, the longer the shoreline of wonder". Learning more about spatial analysis only leads to discovering there is much more to learn. This chapter mostly aims to make you realise this about spatial regression and hopefully tempt you into wanting to continue this journey. In what follows we offer suggestions for this path.

There are a number of accessible, if somehow dated, introductory discussions of spatial regression for criminologists: [205] and [206]. The books by [202], [179], and [180] expand this treatment with the social student in mind. Pitched at a similar level is [192]. More mathematically detailed treatment and a wider diversity of models, including those appropriate for panel data, are provided in several spatial econometric books such as [204], [197] or [207]. In these econometric books you will also find more details about newer approaches to estimation, such as GMM. If you are interested in exploring the Bayesian approach to modelling spatial lattice data, we suggest you start with [178].

There are also a number of resources that focus on R capabilities for spatial regression and that have inspired our writing. It is important to highlight that many of these, even the more recent ones, do not account properly for how spatialreg has deprecated the regression functionality of spdep, even if they still provide useful instruction (for the basic architecture of the functions that have migrated to spatialreg has not been started from scratch). The workbook of [213] offers a detailed explanation of the spatial regression capabilities through spdep, most of which is still transferable to the equivalent functions in spatialreg. This workbook indeed uses the "ncovr" dataset and may be a useful continuation point for what we have introduced here. [196] provides one of the most up-to-date discussions of spatial regression with R also pitched at a level the reader of this book should find accessible. [193] offer a more technical, up-to-date, and systematic review of the evolution of the software available for spatial econometrics in R. It is definitely a must read. For Bayesian approaches to spatial regression using R, which we have not had the space to cover in this volume, we recommend [208], [209], [210], and [211], all with a focus on health data.

Aside from these reading resources, there are two series of lectures available on YouTube that provide good introductions to the field of spatial econometrics. Check out Prof. Mark Burkey’s spatial econometric reboot and Luc Anselin’s lectures in the GeoDa Software channel.

Although the focus of this chapter has been on spatial regression, there are other approaches that are used within crime analysis for the purpose of predicting crime in particular areas such as risk terrain modelling or the use of other machine learning algorithms for prediction purposes. Those are well beyond the scope of this book. Risk terrain modeling [214] is generally actioned through the RTDMx software commercialised by its proponents. In a recent paper, [215] illustrate how random forest, a popular machine learning algorithm, can also be used to generate crime predictions at micro-places. Dr. Gio Circo is currently developing a package (quickGrid) to apply the methods proposed by Wheeler and Steenbeek (2021).