Statistical Inference Of Hierarchical Model Based On Guass-Seidel Type Iterative Algorithm

Missing data phenomenon is a very common problem in observation data,and EM algorithm is a common method for parameter estimation in missing data problem,which transforms incomplete data into complete data problem to deal with.For parameter estimation problem in Hierarchical Linear Regression Model,we often take two-level data model as an example,and use EM algorithm to solve iteratively.The main idea of this thesis is to generate the current latest value by iteration,and use the latest value to calculate the next step of the latest parameter estimation.The parameter estimation of fixed effect and random effect in Hierarchical Linear Model is derived,and the convergence of the iterative process is determined according to the judgment criteria until the end of the iterative process.The main contribution of this thesis is as follows One is to use the Guass-Seidel type iterative algorithm to improve the convergence speed of parameter iteration.To deal with the problem of hypothesis testing in statistical inference,statistical inference is the main method to infer the population through the observation information of sample data.For the coefficient vector diagnosis method of Hierarchical Linear Regression Model with nested structure,the traditional F-test of Linear Nested Regression Model is mainly used to diagnose the coefficient of the first level model of Hierarchical Linear Regression Model.In this thesis,in the statistical diagnosis of the second layer coefficient of Hierarchical Linear Regression Model,we extend the multiple Linear Regression Model with nested structure to the Hierarchical Linear Regression Model with nested structure.We mainly construct the likelihood function ratio of the Hierarchical Linear Regression Model to construct the test statistics to judge the fitting problem of the second layer coefficient vector.Finally,the numerical results of stochastic simulation show that the Guass-Seidel type iterative method has more effective convergence rate than the EM algorithm of Hierarchical Linear Model in literature.The validity and practicability of the statistical inference method of Hierarchical Linear Model with nested structure are illustrated by the data of college mathematics scores.