Statistical Analysis Of Generalized Mixed Effect Model Under Heavy-tailed Process

For the analysis of discrete data,this paper proposes a generalized mixed effect model based on the Student-t(T)process.The correlation between longitudinal discrete data is characterized by a latent T process.This model is used to establish nonlinear random effects.A new framework is provided.The heavy tail of the T process enables reliable inference and the covariance kernel of the process can adaptively capture features on variables.Based on Monte Carlo EM(MCEM)algorithm,an effective estimation result is obtained in this paper,and a prediction method is proposed through conditional inference.Numerical studies show that compared with the Gaussian model,this method is robust to outliers.Finally,this article uses renal anemia data and traffic flow data as examples for analysis.The main research of this master thesis is as follows:The first chapter mainly describes the research background,research phenomena and main work on discrete data studied in this paper,and introduces the normal mixed scale distribution,so as to further introduce the generalized mixed effects model that this paper focuses on,and gives The inference methods mainly involved in this paper are introduced.The second chapter introduces the structure of the T distribution that this article focuses on,and proves that the conditional distribution of the T distribution is still an important property of the T distribution.The research characteristics of some data further give the solution of the truncated T distribution and its related expectations.It provides a theoretical basis for the subsequent statistical analysis of discrete data,and finally gives a generalized mixed effect model under the T process that is the focus of this paper.The third chapter focuses on binary data,and builds a generalized mixed effect model based on the T process.It introduces new latent variables to better explain the meaning of binary data in real life.The construction of the model is based on the traditional Gaussian process model combined with the relevant normal mixed scale distribution,and then makes distribution assumptions for the relevant variables in the model.In the derivation,it is further improved based on the EM algorithm,using MCEM Algorithm for statistical inference,avoiding complex expectations.Then,in the simulation research,the parameters in the model were estimated first.The data types mainly studied were outliers and data from the Gaussian process.The results of the model proposed in this chapter and the Gaussian process model were compared.As well as the predictive effect of related variables,experiments show that the model proposed in this chapter has good robustness.Finally,the use of renal anemia data for example analysis,also using the model proposed in this chapter to get good analysis results,has good practical significance.The fourth chapter mainly focuses on counting data,and also builds a generalized mixed effect model based on the T process.In the derivation of the model,we are the same as the previous chapter based on the relevant theoretical derivation based on the EM algorithm.The complexity of conditional distribution makes it relatively difficult to solve the integral.Therefore,this chapter combines the MCEM algorithm and the MH sampling algorithm for statistical inference.The feasibility of the model proposed in this chapter and the validity of the inferred results are also confirmed through simulation analysis.Finally,the model is applied to traffic flow data,and relatively reliable research results are obtained.Chapter 5 makes a series of conclusions on the model,research methods,conclusions and practical significance of the whole article,and looks forward to the future research on discrete data.