Spatial Association from the Perspective of Mutual Information

Measures of spatial association are important to reveal the spatial structures and patterns in geographical phenomena. They have utility for spatial interpolation, stochastic simulation, and causal inference, among others. Such measures are abundantly available for continuous spatial variables, whereas for categorical spatial variables they are less well developed. In this research, we developed a measure of spatial association for categorical spatial variables coined the entropogram, quantifying its spatial association using mutual information. Mutual information concerns information shared by pairs of random variables at different locations as revealed by their observed joint frequency distribution and marginal frequency distributions. The developed new measure is modeled as a function of lag in analogy to the variogram. Whereas existing measures focus mainly on interstate relationships, the entropogram models the spatial correlation in categorical spatial variables holistically. In this way, the entropogram imparts multiple advantages, for example, simplifying the representation of spatial structure for categorical variables and facilitating communication. The entropogram also reflects variation in the spatial correlation between different states. We first explored the properties of the entropogram in a simulation study. Then, we applied the entropogram to analyze the spatial association of land cover types in Qinxian, Shanxi, China. We conclude that the entropogram provides a suitable addition to existing measures of spatial association for applications in a wide range of disciplines where the categorical spatial variable is of interest.