A Study Of Semi-parametric Spatial Variable Coefficient Models

Based on the traditional linear regression model,spatially varying coefficient model regards the parameters as the function of geographical location,and discusses the different influence mechanism of the explanatory variables on the interpreted variables due to the different spatial location.It has been widely used in many fields with geographical characteristics data.Location information is an important information contained in spatial data.For spatial data,it is important to fully excavate its position information for accurate analysis of the relationship between observation variables,while spatially varying coefficient model can effectively deal with such data.Because of the important position of spatially varying coefficient model in practical research,many scholars have carried out in-depth research on it and achieved fruitful results.Based on previous studies,this paper attempts to further expand the spatially varying coefficient model,and proposes two types of spatially varying coefficient models.Firstly,estimation of a spatial lag mixed geographically weighted regression model is considered.The model considers spatial dependence and spatial heterogeneity at the same time.Based on the profile method and GMM method,three estimation methods are given for the model:Profile GMM Estimation,Efficient GMM Estimation and Two-stage Estimation.For the parameter that need to be set in the model,the reasonable and effective methods are adopted to select the parameters.Finally,the stability of the three estimation methods is proved by numerical simulation.Secondly,a spatially varying coefficient model on panel data is proposed.The variable value of the spatially varying coefficient model is extended to panel data.The coefficient is expressed as the function of time and space,which makes the spatially varying coefficient model increase the time dimension.It can not only analyze the mechanism between the explanatory variable and the explained variable in the same period,but also track the expression of the model in different periods of the same individual,thus expanding the dimension of studying practical problems,the analysis of the problem is also more comprehensive and in-depth.In view of the estimation problem of the model,the virtual variable is introduced and the geographically weighted regression is used to estimate.At the same time,the test statistics for testing the form of the model are given,which is the premise of studying practical problem.The validity of the estimation method and the reliability of the estimation results are verified by numerical simulation.The results of this paper extend the theoretical form and application scope of the spatially varying coefficient model,which is of great reference value to the research of practical problems.