Bayesian Inference In A Class Of Semiparametric Partial Linear Mixed Models For Longitudinal Data

As a kind of data which is widely used in the current scientific research and practical analysis,longitudinal data has appeared quite frequently in clinical medicine,epidemiology,econometrics and many other fields.it contains both time series data and cross section data and can be viewed as a combination of time series data and section data.It can bond research objects which is at different time organically to provide us with the variable relations at a certain point and variation trends of research objects over time to analyze the dynamic change rules of the object better.In the meanwhile,longitudinal data could reduce the heterogeneity between individuals and offer more sample information to effectively lower the collinearity between variables and the higher degree of freedom of the model.Further,we can structure and research more complex models to estimate and determine the correlations between individuals and variables which is hard for single time series data or cross-section data.Aimed to study longitudinal data in depth,statisticians and economists constantly enrich the statistical theory and complete,improve and put forward a series of statistical models.In those models,semiparametric partial linear mixed models have been popularly used due to their prominent advantages.Composite the parametric mixed models with nonparametric mixed models,semiparametric partial linear mixed models set explanatory factors which is relatively clear with response factor into parametric models and set other fuzzy variables(e.g.,time factor,etc.)into nonparametric models.Therefore,this type of models contain parametric and nonparametric segment in the meantime and can be used to describe the relationship between variables and response variables.Hence semiparametric partial linear mixed models have good theoretical values and practical significance and have become a hot issue.This paper mainly analyzes the Bayesian inference in a class of semiparametric partial linear mixed models for longitudinal data,with an emphasis on the Bayesian inference of semiparametric partial linear mixed models and varying-coefficient partial linear mixed models.We first study the Bayesian inference of semiparametric partial linear mixed models for the longitudinal data.Through smoothing spline method to approximate nonparametric component,we transfer the models into the parametric mixed models and derive the posteriori distribution of fixed effects and random effects based on the chosen prior.On account of the posteriori distributions,this paper proposes all the parametric estimators by MCMC method and proceed simulation under different sample to discuss the accuracy of the estimators.Further,we generalize the method to the varying-coefficient partial linear mixed models.Similarly,we transfer the proposed mixed models into the parametric mixed models and derive the posteriori distribution of fixed effects and random effects based on the chosen prior.On account of the posteriori distributions,this paper proposes all the parametric estimators by MCMC method and proceed simulation under different sample to show the accuracy of the estimators.In the end,the paper selects fifty listed real estate companies from the domestic A-share market as research object and choose suitable factors according to the principle of enterprise’s ability to make profit.semiparametric partial linear mixed models set explanatory factors which is relatively clear with response factor into parametric models and set other fuzzy variables(e.g.,time factor,etc.)into nonparametric models.In the next,we put the semiparametric partial linear mixed models and varying-coefficient partial linear mixed models to empirical analysis and give the values of parameters in the model using Bayesian inference.At last,we compare the result of Empirical Stimulation with the actual situation and illustrate the proposed model is fine and effective.