Location-specific cumulative distribution function (LSCDF): An alternative to spatial correlation analysis

Quite often, geographical analysis involves comparing the spatial distributions of two variables or attributes. A typical method is to calculate the correlation coefficient of the two variables for corresponding areal units. Putting aside the fact that correlation coefficient is aspatial in nature (swapping attribute values between spatial units will not alter the value of correlation coefficient) and the issue of spatial dependency (or the potential existence of spatial autocorrelation) among observations, another major problem with using correlation measures for analyzing spatial data is the modifiable areal unit problem (MAUP), especially with the scale effect. Results from correlation analysis vary with the spatial resolutions based upon which spatial data are gathered. This paper presents an approach for spatial correlation analysis for count variables by comparing their cumulative. Using the concept of cumulative distribution function (CDF) in classical statistics, this paper shows that location-specific CDF (LSCDF) and its associated K-S-like statistic, which indicate the magnitude of difference between the two spatial distributions, are highly consistent over different levels of spatial scale. The application of the LSCDF approach is not restricted to isotropic spatial processes and the statistic provides a rather conservative conclusion. In addition, given any origin to construct LSCDFs, the LSCDFs can provide a geographic description of the two spatial distributions. By combining LSCDFs derived from different origins, a comprehensive understanding of the two distributions for the entire study area is der;eloped. This approach for correlation analysis may offer a direction for future investigation of the MAUP.