Local Linear BGWR Estimation And Application Of Spatially Varying Coefficient Models

With the rapid development of society, the observation data is often collected in some specific spatially geographical locations and formed space data set with spatial attributes(like spatial non-stationarity, etc) in many scientific research fields. In recent years, the spatially varying coefficient model get more attention and be used widely with the frequent appearances of non-parametric regression models. This paper studied the spatially varying coefficient regression model from the aspects including of fitting method, the comparison of coefficient function surface figure and applications.Introduced the local linear GWR estimation of spatially varying coefficient model. This paper focused on spatially varying coefficient regression model, constructed a weighted matrix by spatially weighted distance, and obtained the local linear Bayesian geographical weighted regression(BGWR) estimation method based on the Bayesian inference and statistical computing of multiple linear regression model. Then the posterior distribution of regression coefficients were deduced by means of this method, and the pointwise estimation of regression coefficients were calculated thought the Gibbs sampling method. Finally, compared the results with LeSage BGWR model estimation by mapping surface, calculating deviation means and standard deviation means of the outcomes, the effectiveness of this estimation method was further illustrated.Finally, we use spatially varying coefficient model to study an instance of ecology. Based on the spatially varying coefficient regression model, this study analyzed the spatial variation characteristics of the vegetation coverage index in response to precipitation and temperature in the Yili area of Xinjiang in 2006 and 2011. The regression coefficient map estimated by using the local linear BGWR method further revealed that the spatial heterogeneity of the interaction between the variables.The results were compared against LeSage BGWR model estimation. The main findings are the following: 1)The spatially varying coefficient regression model can be used to analyze the spatial correlation between variables. 2) The local linear GWR is superior to the LeSage BGWR model estimation. 3) Results showed a clearly spatial non-stationary characteristics of the vegetation coverage index under the effects of precipitation and temperature in the Yili area of Xinjiang. 4) In addition to precipitation and temperature, factors such as topography, geomorphology and human activities can cause deviations in the estimation, which requires further research. This paper provides new ideas and methods to analyze spatial correlation between variables that exhibit spatial non-stationary characteristics and to obtain spatial simulation distribution of the vegetation coverage index.