Bayesian Analysis Of A Class Of Generalized Partial Linear Mixed Effect Model For Longitudinal Data

Longitudinal data are very common in many fields,such as psychology,epidemiology,economics,sociology and so on.It is an important data format of actual analysis and subject research at present.Longitudinal data is a repeated measure of data for a group of individuals in time or space order.For the processing of longitudinal data with heteroscedasticity which does not satisfy normal distribution,the generalized linear or partial linear mixed model is used to fit the data.It is usually used to estimate the global or local estimation methods of nonparametric components in a generalized partial linear mixture model,which need smooth parameters,which not only increases the burden of the model estimation,but also makes the statistical inference of the model parameter estimation difficult.In order to overcome the above problems,this paper selects Bayesian method for analysis,because the Bayesian method introduces the prior information,so it can get relatively reliable results when the sample is less.At the same time,in order to simplify the complexity of the posterior distribution and improve the computational efficiency,this paper simplifies the prior assumption of the part of the model random effect,assuming it obeys the normal distribution.We first analyze the generalized semi parametric partial linear mixed effect model under the longitudinal data.The semi parametric generalized partial linear mixed effect model is transformed into a generalized linear mixed effect model by the spline method,and then the posterior distribution is derived based on the penalty spline and the smooth spline.Based on the obtained posteriori distribution,we use the Gibbs and MH hybrid algorithm to give the Bayesian estimation of the parameters in the model,analyze the accuracy of the estimated parameters,and compare the estimation efficiency of the smooth spline and the penalty spline.Further,we extend the above method to Bayesian inference of variable coefficient generalized partial linear mixed effect model.In addition,based on the longitudinal data of 12 Chinese A shares listed companies from 2004 to 2011,the semi parametric generalized partial linear mixed effect model and variable coefficient generalized partial linear mixed effect model are selected to analyze the cash dividend payment tendency of China's A share listed companies from the aspects of growth,management and stock ownership structure.Sound factors.Finally,the effectiveness of the proposed model is proved by empirical analysis.