On the calibration of multiscale geographically and temporally weighted regression models

Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.