Bayesian Quantile Regression And Its Application In Generalized Linear Mixed Effects Models

Different types of aggregated data widely exist in practical analysis,such as normal longitudinal data,binary longitudinal data,counting longitudinal data and so on.In order to draw regular conclusions from seemingly disordered observation data,we often need to resort to statistical models.The traditional model assumes that the observation samples are independent of each other,and the fitting effect of the traditional model on the longitudinal data is very poor.This paper combines the characteristics of linear mixed effect model which can process longitudinal data and generalized linear model which can process binary and counting data.The generalized linear mixed effect model is used to model different types of longitudinal data.When estimating the model parameters,we combine the robustness of the fractional regression and the advantages of Bayesian analysis.Based on the asymmetric Laplce distribution,we establish a Bayesian quantile regression suitable for the generalized linear mixed effect model.In the Bayesian solution of the hypothetical model parameters,it is difficult to calculate the posteriori of the parameters because the asymmetric Laplce distribution does not have an appropriate priori.We use M-H algorithm and Gibbs sampling algorithm in common MCMC algorithm to estimate the parameters.In method simulation,Gibbs sampling algorithm performs very well in sample implementation,software operation and parameter estimation results.We use Gibbs sampling algorithm to analyze the actual data of binary longitudinal data.The method used in this paper not only provides a good model selection,but also provides a good parameter estimation method and algorithm for different types of longitudinal data modeling problems.Gibbs sampling algorithm,with its superior performance,deserves to be widely applied in actual data analysis.