Spatially Varying Coefficient Elastic Net Model And It's Application

With the expansion of information resources today,a hot issue in the field of data analysis is how to deal with complex data.With the development of technology and economy,many fields would face a huge challenge which is how to process data with a large amount of storage and high dimensionality efficiently.In summary,these complex data generally have high dimensionality,dependent variables,or sparse key influencing factors.In this case,dealing with collinearity and variable selection issues becomes more and more important.The variable coefficient model is a powerful tool to explore the dynamic characteristics of the regression relationship between variables.Its various derivative models and statistical inference theories have been fully studied and are widely used in the fields of economy and finance,ecological environment and epidemiology.High-dimensional data and collinearity issues bring new challenges to the effective application of the model.At present,the research on variable selection of variable coefficient regression models is in the ascendant,mainly for non-parametric parts using local quadratic approximation algorithms to achieve irrelevant or low correlation variables.The shrinkage estimation fails to make full use of the computational advantages of parameter sparsity.Moreover,when the parameter dimension is high or there is correlation or even collinearity between variables,the matrix may appear ill-conditioned or even irreversible during the calculation process.The introduction of elastic net penalty intends to solve this problem.Elastic net penalty is a convex combination of Lasso penalty and ridge regression penalty.Lasso penalty realizes the sparse expression of the model.The latter includes ridge regression penalty,which effectively copes with the multicollinearity existing between multiple variables so as to accurately identify the model structure and to improve the interpretability of the model in application.First,the thesis introduces the elastic net penalty term into the variable coefficient regression model framework.It proposes the variable coefficient elastic net regression model(VCM-EN).After combining local linear and coordinate descent algorithms for variable selection and feature extraction,it effectively uses the sparse coefficient function and avoids the ill-conditioned or irreversible estimation matrix.Then it compares with variable coefficient ridge regression(VCM-R)and variable coefficient Lasso(VCM-L)methods,and it does simulation experiments and empirical analysis.The results show that it is feasible to implement the elastic net method to shrink the regression coefficients under the framework,and it found that when there is collinearity between the variables,the VCM-EN method tends to retain the two influencing factors at the same time,which can more accurately identify the important influence on the response variable.The factors are better explanatory in practical applications.Finally,the VCM-EN method was extended to the space,and the spatial variable coefficient elastic net regression model(GWEN)was proposed to study the variable selection and structure identification of the high-dimensional regression model of spatial data.Simultaneous experiments and comparative analysis were done at the same time,and the model was used.The spatial data set of hand,foot and mouth disease is analyzed.The results show that the GWEN model not only has the estimation accuracy of the geographically weighted model(GWR),but also has the advantages of the elastic net model(EN)explanatory variable multicollinearity,which provides new ideas for the analysis of complex spatial data.