  The idea of spatial crosscorrelation was conceived of long ago. However,
unlike the related spatial autocorrelation, the theory and method of spatial
crosscorrelation analysis have remained undeveloped. This paper presents a set
of models and working methods for spatial crosscorrelation analysis. By analogy
with Moran's index newly expressed in a spatial quadratic form and by means of
mathematical reasoning, I derive a theoretical framework for geographical
crosscorrelation analysis. First, two sets of spatial crosscorrelation
coefficients are defined, including a global spatial crosscorrelation
coefficient and a set of local spatial crosscorrelation coefficients. Second, a
pair of scatterplots of spatial crosscorrelation is proposed, and different
scatterplots show different relationships between correlated variables. Based
on the spatial crosscorrelation coefficient, Pearson's correlation coefficient
can be decomposed into two parts: direct correlation (partial crosscorrelation)
and indirect correlation (spatial crosscorrelation). As an example, the
analytical process is applied to the relationships between China's urbanization
and economic development. Spatial crosscorrelation and spatial autocorrelation
can complement one another, and the spatial crosscorrelation scatterplots can
be used to reveal the causality inside a self-organized system. The spatial
crosscorrelation models will play a useful role in future geographical spatial
analysis.
