Chapter 18 Multivariate Local Spatial Autocorrelation

In this chapter, the concept of local spatial autocorrelation is extended to the multivariate domain. This turns out to be particularly challenging, due to the difficulty in separating spatial effects from the pure attribute correlation among multiple variables.

Three methods are considered. First, a bivariate version of the Local Moran is introduced, which, similar to what is the case for its global counterpart, needs to be interpreted with great caution. Next, an extension of the Local Geary statistic to the multivariate Local Geary is considered, proposed in Anselin (2019a). The final approach is not based on an extension of univariate statistics, but uses the concept of distance in attribute space, in the form of a Local Neighbor Match Test (Anselin and Li 2020).

To illustrate these methods, the Chicago SDOH sample data set is employed. It contains observations on socio-economic determinants of health in 2014 for 791 census tracts in Chicago (for a detailed discussion, see Kolak et al. 2020).