基于嵌套结构的分层线性回归模型的统计推断

Statistical Inference of Hierarchical Linear Regression Model Based on Nested Structure

摘要: 通常在处理模型假设检验的问题时，统计推断是通过样本数据的观测信息来推断总体的主要方法，本文提出基于嵌套结构的分层线性回归模型的系数向量诊断方法，对于分层线性回归的第一层模型系数诊断主要利用传统的线性嵌套回归模型F检验进行统计推断。该论文的创新之处在于对分层线性回归模型的第二层系数进行统计诊断，利用嵌套多元线性回归模型推广到具有嵌套结构的分层线性回归模型中，主要构建分层线性回归模型似然函数比值来构造检验统计量。通过高校数学成绩分层数据进行分析，来验证该方法的有效性和可行性。

Abstract: Generally, when dealing with the problem of model hypothesis testing, statistical inference is the main method to infer the population through the observation information of sample data. In this paper, the coefficient vector diagnosis method of Hierarchical Linear Regression Model based on nested structure is proposed. For the first level model coefficient diagnosis of hierarchical linear regression, the traditional F-test of linear nested regression model is used for statistical inference. The innovation of this paper lies in the statistical diagnosis of the second layer coefficient of Hierarchical Linear Regression Model. The nested multiple linear regression model is extended to the Hierarchical Linear Regression Model with nested structure. The likelihood function ratio of Hierarchical Linear Regression Model is mainly constructed to construct the test statistics. The effectiveness and feasibility of this method is verified by the hierarchical data analysis of college mathematics scores.