Spatial Interaction Models and Spatial Dependence

Spatial interaction models of the types discussed in the previous chapter take the view that inclusion of a spatial separation function between origin and destination locations is adequate to capture any spatial dependence in the sample data. LeSage and Pace (J Reg Sci 48(5):941–967, 2008), and Fischer and Griffith (J Reg Sci 48(5):969–989, 2008) provide theoretical as well as an empirical motivation that this may not be adequate to model potentially rich patterns that can arise from spatial dependence. In this chapter we consider three approaches to deal with spatial dependence in origin–destination flows. Two approaches incorporate spatial correlation structures into the independence (log-normal) spatial interaction model. The first specifies a (first order) spatial autoregressive process that governs the spatial interaction variable (see LeSage and Pace (J Reg Sci 48(5):941–967, 2008)). The second approach deals with spatial dependence by specifying a spatial process for the disturbance terms, structured to follow a (first order) spatial autoregressive process. In this framework, the spatial dependence resides in the disturbance process (see Fischer and Griffith (J Reg Sci 48(5):969–989, 2008)). A final approach relies on using a spatial filtering methodology developed by Griffith (Spatial autocorrelation and spatial filtering, Springer, Berlin, Heidelberg and New York, 2003) for area data, and leads to eigenfunction based spatial filtering specifications of both the log-normal and the Poisson spatial interaction model versions (see Fischer and Griffith (J Reg Sci 48(5):969–989, 2008)).