Geographical and temporal density regression

Abstract

Spatial heterogeneity and correlation are two primary geographical effects of spatial data. Geographically weighted regression (GWR) and its extensions were proposed to quantitively analyze the heterogeneous features in data relationships. An integrative distance metric is usually adopted to calculate proximity-based weights for model calibration for these techniques. However, it could be defective when dealing with higher dimensional data, eg spatio-temporal data (3-D), and geographical flow data (4-D). This study proposes a new local model, namely geographical and temporal density regression (GTDR), to deal with objects of flexible dimensions by reconsidering the spatial weights and experimental investigation of GWR. We use a Nelder-Mead algorithm to optimize each kernel function’s bandwidth for every dimension. To validate its performance, we conduct three sets of simulation experiments with 2-D, 3-D, and 4-D data, respectively, and compare them to conventional techniques. Results indicate the apparent advantages of GTDR in treating each dimension individually instead of calculating an integrative distance in traditional ways, such as spatio-temporal or flow distances. All in all, the GTDR technique shows a promising ability in fitting data with higher and diverse dimensions, and exploring heterogeneities in temporal, spatial, spatio-temporal or more complex structural data relationships.