Bayesian Analysis For Several Classes Of Skew-Normal Semiparametric Partially Linear Random-Effects Models

The statistical model for longitudinal data is one of the hotspots in modern statistical research,and it has a wide range of applications in fields such as economic management,biomedicine,and public health.In the Bayesian framework,we propose several types of skewnormal semiparametric partially linear random-effects models in the analysis of discrete and continuous longitudinal data,and investigate their corresponding parameter estimation,variable selection,and local local influence analysis.The main research results are as follows:(1)In the relevant literature research of the semiparametric generalized partially linear random-effects models,the random-effects are usually assumed to follow a specific distribution such as normal distribution.However,in practical problems,the longitudinal data often show the characteristics of skewness and thick tail,etc,and the normal distribution assumption of random-effects may lead to the deviation of the conclusion from the real problem.Therefore,we introduce the skew-normal distribution to model the random-effects in generalized partially linear random-effects models,and construct a new type of model: skew-normal semiparametric generalized partially linear random-effects models.The Bayesian P-spline method is used to approximate the nonparametric function 2)(·)of the models.Further,the Bayesian adaptive Lasso variable selection method and the least squares approximation(LSA)method based on the linear regression models are extended to the skew-normal semiparameter generalized partially linear random-effects models,and the variable selection and parameter estimation of the model are done at the same time.Finally,we obtain the joint Bayesian estimate of unknown parameters,skew-normal random-effects and nonparametric function 2)(·)and the variable selection of covariates of this models by combining with the block Gibbs sampler,MH algorithm and the hybrid algorithm of Bayesian adaptive Lasso.(2)We extend the semiparametric generalized partially linear random-effects models to a more widely used complex model,namely,the semiparametric reproductive dispersion partially linear randomeffects models.We introduce the skew-normal distribution to model the random-effects in the semiparametric reproductive dispersion partially linear random effects models,and construct a new model: the skew-normal semiparametric reproductive dispersion partially linear random-effects models.At the same time,we use Bayesian Psplines to approximate the nonparametric function 2)(·)of the model.Under the Bayesian framework,we use the prior distribution of parameters and the information provided by the sample to derive the posterior distribution of parameters,and develop a hybrid algorithm combining block Gibbs sampler and MH algorithm,while obtain the joint Bayesian estimation of the unknown parameters,randomeffects and nonparametric function 2)(·)of this model.(3)Based on the Bayesian estimation results of the skew-normal semiparametric reproductive dispersion partially linear random-effects models and the research theory of Zhu et al.(2011),we construct a set of Bayesian local influence analysis methods to evaluate the sensitivity of the skew-normal semiparametric reproductive dispersion partially linear random-effects models to individual data,prior distribution and sample distribution simultaneously small disturbance.Firstly,we construct the Bayesian disturbance manifold for the model,and construct the tangent space and calculate the metric tensor on the perturbation manifold to select the appropriate perturbation model.Secondly,we develop Bayesian local influence measures for objective functions(such as -Divergence statistic,Posterior Mean Distance statistic,Bayes Factor),and develop some easyto-implement algorithms to calculate these Bayesian local influence measures.In conclusion,we obtain some new results based on the study of semiparametric generalized partially linear random-effects models and semiparametric reproductive dispersion partially linear randomeffects models,which popularize and develop some of the existing research work on these types of model,and these results are of concern in theory and also have important application value in practice.Finally,the effectiveness of the extended and developed methods is showed through simulation studies and example analysis.