Geographically weighted regression based on a network weight matrix: a case study using urbanization driving force data in China

Geographically weighted regression (GWR) is a classical modeling method for dealing with spatial non-stationarity. It incorporates the distance decay effect in space to fit local regression models, where distance is defined as Euclidean distance. Although this definition has been expanded, it remains focused on physical distance. However, in the era of globalization and informatization, where the phenomenon of remotely close association is common, physical distance may not reflect real spatial proximity, and GWR based on physical distance has clear limitations. This paper proposes a geographically weighted regression based on a network weight matrix (NWM GWR) model. This does not rely on geographical location modeling; instead, it uses network distance to measure the proximity between two regions and weights observations by improving the kernel function to achieve distance attenuation. We adopt the population mobility network to establish a network weight matrix, modeling China's urbanization and its multidimensional driving factors using network autocorrelation and NWM GWR methods. Results show that the NWM GWR model has more accurate fit and better stability than ordinary least squares and GWR models, and better reveals relationships between variables, which makes it suitable for modeling economic and social systems more broadly.