Statistical Inference Of Simplex Semiparametric Linear Mixed Effects Model With Nonignorable Missing Data

This paper discusses the Bayesian estimation of parameters and model selection in the simplex semiparametric linear mixed effects model with nonignorable missing response variables.The semiparametric linear mixed effect model contains not only fixed effect and random effect,but also parametric part and nonparametric part.The simplex semiparametric linear mixed effect model that the response variables follow the simplex distribution,and its position parameters are characterized by the semiparametric linear mixed effect model.In this paper,firstly,a simplex semiparametric linear mixed effect model is given,and its mean value is characterized by a link function and a semiparametric linear mixed effect model.For the nonparametric part of the semiparametric linear mixed effect model,Bayesian spline is used to approximate the unknown smooth function.This paper assume that the response variable is missing,and the missing data mechanism is nonignorable,the Logistic regression model is used to model the missing mechanism.In order to obtain the Bayesian estimation of the parameters in the model,based on the posterior conditional probability density function of the parameters,combined with Gibbs sampling and MH algorithm,this paper give the Bayesian estimators of the parameters.In order to select the correct model,path sampling is used to calculate the Bayes factor.In this paper,four simulation experiments are carried out to show the effectiveness of the methods.Simulation experiment 1 shows that Bayesian estimation is not sensitive to the priori information;simulation experiment 1 and simulation experiment 3 show that under different sample sizes,the method in this paper can get better results;simulation experiment 1 and simulation Experiment 2 shows that Bayesian estimation does not depend on the distribution of explanatory variables;in simulation experiment 4,the correct model is selected.The above results show that the methods proposed in this paper are effective.