Applying Local Indicators of Spatial Association to Analyze Longitudinal Data: The Absolute Perspective

Abstract

Local Indicators of Spatial Association (LISA) are a class of spatial statistical methods that have been widely applied in various scientific fields. When applying LISA to make longitudinal comparisons of spatial data, a common way is to run LISA analysis at each time point, then compare the results to infer the distributional dynamics of spatial processes. Given that LISA hinges on the global mean value that often varies across time, the LISA result generated at time T_i reflects the spatial patterns strictly with respect to T_i. Therefore, the typical comparative cross-sectional analysis with LISA can only characterize the relative distributional dynamics. However, the relative perspective alone is inadequate to comprehend the full picture, as the patterns are not directly associated with the changes of the spatial process’s intensity. We argue that it is important to obtain the absolute distribution dynamics to complement the relative perspective, especially for tracking how spatial processes evolve across time at the local level. We develop a solution that modifies the significance test when implementing LISA analysis of longitudinal data to reveal and visualize the absolute distribution dynamics. Experiments were conducted with Mongolian livestock data and Rwanda population data.