Research On Geographically And Temporally Weighted Regression For Spatial And Temporal Nonstationarity

The analysis of spatial and temporal nonstationary could not only reveal the spatial and temporal distribution of geographical factors, but also understand the dynamic process of social phenomena and the environment. Geographically and temporally weighted regression (GTWR) incorporates the spatial and temporal impact into the geographically weighted regression and solves both spatial and temporal nonstationarity issues. Firstly, this paper proposes the weighted condition index and variance decomposition proportions (WCIVDP) to diagnose the GTWR multicollinearity. Secondly, after the spatial and temporal test was implemented, this thesis proposes the two-stage least square approach to estimate the GTWR model. Thirdly, this paper proposes the semi-supervised geographically and temporally weighted regression (SSGTWR) method to improve the prediction precision. The main contents and innovations of this research are as follows:(1) The GTWR model could consider both the spatial and temoporal nonstationarity. Therefore, this paper introduces the basic theories of GTWR which contains the selection of optimal spatial bandwidth, spatial-temporal parameter and the construction of spatial-temporal kernel function. To reduce the number of sptial and temporal parameters, the theories of optimal spatial-temporal factor selection have been explained.(2) The proposed WCIVDP method could diagnoze the multicollinearity of GTWR model and the test of spatial and temporal nonstationarity has been implemented. The global approach of diagnozing the multicollinearity would neglect the local multicollinearity. The experiment shows that the WCIVDP could not only achieve the number of multicollinearity and the columns of the design matrix, but also diagnoze the multicollinearity of intercept.(3) Two stage least square approach is proprosed to estimate the geographically and temporally weighted autoregressive regression (GTWAR) model. The least square approach could not be used to estimate the GTWAR model. The maximum likelihood approach to estimate the large sample data will generate a large matrix, resulting in a long time. The two stage least square method does not require random error to meet the independent and identically distributed, and can significantly reduce the computational complexity. Therefore, this paper takes the Beijing housing sales price as an example, and puts forward the two stage least square estimation method of GTWAR model. The results of the experiment have been analyzed from Moran' I, variance analysis, the goodness of fit analysis and the regression coefficient. The experimental results show that the GTWAR model achieves the best fitting results.(4) The proposed semi-supervised geographically and temporally weighted regression (SSGTWR) approach could significantly improve the small sample estimation accuracy when dealing with the regression and analysis issues. The semi-supervised paradigm was often adopted to absorb the unlabeled data in the machine learning field. However, the spatial-temporal characteristics was not considered using the traditional regressors. Therefore, this paper uses the GTWR model to establish the spatial regressors and absorb the most confidential unlabeled data. The simulated data and Beijing Hedonic house price data have been used to evaluate the proposed approach. The results show that, comparing with the traditional results, the SSGTWR approach could absorb the unlabeled spatial data to establish stable spatial regressors and improve in the RSS, MSE and AIC. The proposed method could be applied in the broad spatial analysis field.