Section 12.3 Summary and further reading
This chapter has tackled some of the issues of spatial heterogeneity in regression results. When applying regression in a spatial context, it is possible to encounter situations where we might observe a different effect on our variables in different parts of our study area. Specifically, we covered two approaches to exploring this. The first one was to impose some a priori segmentation to our data, based on contextual knowledge and possible patterns in our regression results. We illustrated this by imposing spatial regimes in our NCOVR data set, splitting into separate North and South USA, as was done by the original authors of the paper by [Baller et al. (2001)]. The second approach was to explore how the coefficients may vary across our study space by applying Geographically Weighted Regression to our study area. We provided a high-level overview of this process and recommended it as an illustrative, exploratory technique to raise questions about possible spatial heterogeneity in the processes we are trying to model in our study region.
To delve into greater detail on the topic of spatial heterogeneity, chapters 8 and 9 in [Anselin (2007)] discuss specification of spatial heterogeneity. This is particularly helpful as an introduction to the issues and solutions we have discussed in this chapter. For more details and applications of Geographically Weighted Regression, we recommend [Fotheringham et al. (2003)]. For applications and an illustration of the importance to consider spatial variation within the context of criminology and crime analysis, read [Cahill and Mulligan (2007)] and [Andresen and Ha (2020)] as good examples.
And for those wishing to explore additional ways to model spatial interactions, such as CAR and Bayesian models, we suggest to read [Banerjee et al. (2014)] as well as chapters 9 and 10 in [Bivand et al. (2013)].
