Application Of Variable Selection In Multi - Level Model To Farmers' Per Capita Income Data

Society is an entirety with hierarchy structure, so the data with hierarchy structure features widely exists in the social studies, in order to processing of such data more accurately, multi-level model arises at the historic moment as a new statistical model. Multi-level model can not only handle the relationship of variables among different levels and across levels at the same time, but also can explore the influence of characteristics in unit level on explained variable, considering the error term between different levels, and then estimated the differences of all levels. Linear Mixed model is an important statistical model that contains both fixed effects and random effects, as it only retained normality assumption of explained variable in general linear model, do not need independence assumption and homogeneity of variance assumption, allow correlation and heteroscedasticity between response variable, so it applicable in repeat observation data, hierarchical structure data and many other actual datas. And the multi-level model can be viewed as a special kind of linear mixed model, when all levels in multi-level model gather into a general model, then the multi-level model have the forms and features of the linear mixed mode.In dealing with practical problems, the first problem we need to solve is model selection, and as an important means of model selection, variable selection is an important content in statistical analysis and inference. The research of variable selection has a long history, with the continuous development of statistical theory and computer technology, variable selection method is gradually increasing and has been more mature variable selection criteria. However, most research of variable selection methods are based on the traditional linear model, the study of variable selection problem for linear mixed model is relatively small, especially for multi-level model, or those methods cannot make variable selection both in fixed effects and random effects at the same time in linear mixed model, and whether the structure of the fixed effects or the random effects changed, it will make the results of variable selection quite different on other part.In this paper, we will rewrite the multi-level model into linear mixed model based on the characteristics of linear mixed model, then decomposition the model with adaptive Cholesky decomposition, and based on Lasso method which joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects of multi-level model. Finally, we applied this method to make an empirical analysis of household income of Honghe data, so that the theory and application of multi-level model more complete and comprehensive.