Spatial Lag Quantile Regression Models For Compositional Data And Its Application

Spatial econometric models can deal with the spatial dependence and spatial lieterogeneity of variables.The spatial lag model is a very important model in spatial economietrics.which can analyze issues such as regional economic development,spatial spillover and spatial agglomeration.Compositional data are a class of complex data with fixed sum constraints,which focus on the proportion of parts in the whole.Quantile feature of the conditional response variable in regression model can be well depicted using the quantile regression.Spatial lag quantile regression models based on compositional data can characterize the entire conditional distribution more completely.and are more robust than spatial mean regression models.Composite quantile regression can use information of multiple quantile points,which can more comprehensively describe the conditional distribution characteristics of the data,and its estimation results are more robust.In this paper.we generalize quantile regression and composite quantile regression to the spatial lag model for compositional data.Due to the characteristics of compositional data,the construction of the model is more complicated.Therefore,we propose the spatial lag quantile regression model and the spatial lag composite quantile regression model following the characteristics of compositional data and spatial data distribution,and discuss its estimation method.Firstly,we perform log ratio transformation to establish the linear log-contrast model.On this basis,we propose constrained two-stage quantile regression,composite quantile regression and instrumental variable quantile regression,composite quantile regression estimation methods.And we compare them with traditional unconstrained estimat,ion methods.Numerical simulations show that our proposed methods are more accurate.We apply the methods t.o real data,and we study the effect of the compositional data of different employment types on votes from the 2015 French departmental election.The results of empirical analysis prove that the NMSE of our proposed estimation method is smaller than that without linear constraints.