The Research Of Random Effects Panel Data Models Based On Bayesian Methed

The panel data model with mixed effect is one of the most widely used models in the current economic statistics research.On the basis of a large number of literatures,the paper puts forward the theory and application research of panel data based on Bayesian method.The problems of parameter estimation and variable selection are discussed from four aspects:Bayesian mean regression,Bayesian regularization mean regression,nonparametric Bayesian quantile regression and Bayesian regularization quantile regression.Six sampling algorithms are proposed under different priori and random error distributions,which are demonstrated and analyzed in theory,simulation and application respectively.The main results are as following.Firstly,for the mean regression panel data models based on Bayesian method,the posterior distribution of each parameter is deduced under the condition that the error and random effect subject to normal distribution,and other parameters have a conjugate prior.Since the posterior distribution is coming from common distribution,a Gibbs sampling algorithm is proposed,and computer simulation is carried out to compare Bayesian mean estimation with traditional methods.Finally,the real data is analyzed by the method in this chapter.Secondly,for the panel data models based on Bayesian regularization method,the paper discussed the selection of important explanatory variables from the perspective of penalty function.It not only can avoid over-fitting but also can avoid under-fitting.The Bayesian Lasso penalty model is established by assuming the regression coefficient subject to Laplace distribution instead of normal distribution,and a MH algorithm and an easy-to-sample Gibbs algorithm is constructed by using integral identities.Considering different explanatory variables are different in models,the same penalty coefficient will bring a big deviation to the important explanatory variables.This paper proposed a Bayesian adaptive Lasso method.The estimator can automatically capture the information of explanatory variables and adopt different penalty coefficients to them.Under different models,we compared the proposed method with Lasso and adaptive Lasso penalty methods.The results show that our methods are superior to them.Finally,we use the Bayesian regularization method in this chapter to estimate the parameters and choose the variables of the wage data.Thirdly,for the nonparametric Bayesian quantile regression model,a finite mixed normal distribution is introduced by relaxing the assumption of random error.The mixed proportion parameters have extensive and flexible Stick-Breaking priors,which are more powerful to capture the information of complex data.By introducing latent variables,a nonparametric Bayesian hierarchical quantile regression model is established.The conditional posterior distribution of each parameter is derived,and then a Gibbs sampling algorithm is proposed.Nonparametric Bayesian quantile regression is more advantageous and flexible than parametric Bayesian quantile regression in complex data models.Under five different simulation data producing models,we compared the nonparametric Bayesian quantile regression with the general and parametric Bayesian quantile regression at median and extreme quantile.Finally,the real data is analyzed by Bayesian quantile regression method.Fourthly,the Bayesian regularization quantile regression model is studied.A Bayesian hierarchical and quantile regression model is constructed by assuming that the random error is an asymmetric Laplace distribution,and the posterior distribution function of the parameters at any quantile can be obtained.By introducing an auxiliary variable,a slice Gibbs sampling algorithm is constructed to estimate the parameters.This method can deal with the posterior distribution of parameters flexibly and is not affected by random effects.The general quantile regression,Lasso-penalized quantile regression,Bayesian quantile regression and two Bayesian Lasso-penalized quantile regression methods proposed in this paper are compared by computer simulation.Six methods presented in this paper are presented and compared in operation time.Finally,the real data is analyzed by the method of Bayesian regularized quantile regression.In the end of this paper,the advantages and disadvantages of the various methods and their application premise are summarized and further research work is put forward.