Theory And Application Of Multiscale Geographically And Temporally Weighted Regression Model

Spatiotemporal non stationarity is ubiquitous in spatiotemporal data and cannot be explained by global models.Geographic weighted regression model(GWR)and geographically and temporally weighted regression(GTWR)solve this problem.GWR and GTWR assume that all variables fit on the same spatial and temporal scales,The spatial-temporal nonstationarity of regression relationship is measured by a single bandwidth.Scale effect describes the spatial range of spatial object attributes and their interactions,which plays an important role in spatial geography research.In fact,long-term spatial analysis practice has found that the influence patterns of different independent variables on dependent variables are closely related to spatial and temporal scales,and have scale dependence.However,the GWR model and GTWR model have obvious limitations because they do not consider the scale effect.In recent years,scholars begin to understand and study the scale effect gradually,and have carried out a series of scale expansion studies on the GWR Model.However,there are few models and methods that can study the spatiotemporal scale effect at the same time.Firstly,considering the spatial scale effect of different variables,the multiscale geographically weighted regression(MGWR)model is studied,and the fitting effect of MGWR model is analyzed through simulation experiments.The MGWR model considering the scale effect uses the back-fitting algorithm to estimate the regression coefficient surface,and selects an optimal bandwidth for each regression variable,MGWR model is better than GWR Model in reducing ability and fitting effect of coefficient surface.Secondly,considering the spatial scale and temporal scale of regression relationship,the GTWR model and MGWR model are combined and extended to study the multiscale geographically and temporally weighted regression(MGTWR).The model selects the optimal time bandwidth and spatial bandwidth for each covariate respectively,so as to identify the multi-scale effect of spatiotemporal process,which is more flexible and interpretable,MGTWR model takes into account the time variability of regression relationship,and can explore the characteristics of the interaction and influence of variables changing with time.Through systematic simulation experiments,the fitting effects of MGTWR and GTWR models are compared,and the results show that MGTWR model is superior.Finally,the relationship between the incidence of hand foot mouth disease and meteorological factors in Xinjiang in 2018 was studied by using MGWR model and MGTWR model.The results showed that:(1)the epidemiological characteristics of HFMD had obvious time heterogeneity,and the incidence rate was reached its peak at month of 5 ～ 8 and reached its second peak at month of 9 ～ 11.(2)the incidence of HFMD had significant spatial heterogeneity,and the incidence rate in eastern and Northern Xinjiang was higher.(3)the incidence of HFMD has a significant scale dependence.That is,in different geographical locations,the meteorological factors have great difference in the incidence rate.Under the different time conditions of the month,the same location is greatly influenced by meteorological factors.With the change of time,the same meteorological factors play different roles in the same location.