A Mixed Geographically and Temporally Weighted Regression: Exploring Spatial-Temporal Variations from Global and Local Perspectives

Abstract

Abstract:To capture both global stationarity and spatiotemporal non-stationarity, a novel mixed geographically and temporally weighted regression (MGTWR) model accounting for global and local effects in both space and time is presented. Since the constant and spatial-temporal varying coefficients could not be estimated in one step, a two-stage least squares estimation is introduced to calibrate the model. Both simulations and real-world datasets are used to test and verify the performance of the proposed MGTWR model. Additionally, an Akaike Information Criterion (AIC) is adopted as a key model fitting diagnostic. The experiments demonstrate that the MGTWR model yields more accurate results than do traditional spatially weighted regression models. For instance, the MGTWR model decreased AIC value by 2.7066, 36.368 and 112.812 with respect to those of the mixed geographically weighted regression (MGWR) model and by 45.5628, −38.774 and 35.656 with respect to those of the geographical and temporal weighted regression (GTWR) model for the three simulation datasets. Moreover, compared to the MGWR and GTWR models, the MGTWR model obtained the lowest AIC value and mean square error (MSE) and the highest coefficient of determination (R 2 ) and adjusted coefficient of determination (R 2 adj ). In addition, our experiments proved the existence of both global stationarity and spatiotemporal non-stationarity, as well as the practical ability of the proposed method.

Water quality and spatio‐temporal hot spots in an effluent‐dominated urban river

“…where the range parameter r controls the spatio-temporal extent of the correlation. Following Liu et al (2017), we defined the spatiotemporal distance d st between a location s i on the river on day t i and another location s j on day t j as a combination of the spatial distance js i − s j j (kilometres) and temporal distance jt i − t j j (days),…”

A Spatiotemporal Deformation Modelling Method Based on Geographically and Temporally Weighted Regression

“…Given a significant level of α � 0.05, the above five hypothesis tests were tested separately. If some regression coefficients in the above tests are spatiotemporal stationary, a mixed geographically and temporally weighted regression model needs to be established [23].…”

The Best Global and Local Variables of the Mixed Geographically and Temporally Weighted Regression Model

“…On the other hand, modeling of poverty data with MGTWR was also carried out by Yasin et al (2015). Liu et al (2017) comparing the MGWR, GTWR, and MGTWR methods based on the exploration of temporal-spatial variations from a global and local perspective.…”

“…Similar to the MGWR model, the MGTWR model contains several coefficients of explanatory variables, assumed to be constant for all observation while other coefficients vary according to the location of the observation. The MGTWR model can be expressed as follows (Liu et al, 2017):…”

“…with and are balancing parameter to the effect of the scale difference between location and time on spatial-temporal distance measurement (Huang et al, 2010). Based on Liu et al (2017), For example is a parameter ratio of = ⁄ with ≠ 0, we get the following equation:…”