Collaborative Research: Variable Selection for Mixed Effect Models

合作研究：混合效应模型的变量选择

• 批准号: 0631652
• 负责人: Ying Lu
• 金额: $ 10.83万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0631652&HistoricalAwards=false
• 关键词: Collaborative; Research; Variable; Selection; Mixed

Most research questions in social science involve complex interactions between individual behaviors and the social contexts. For this purpose, linear and generalized linear mixed effect models have been widely used. Social science applications of mixed models often start with a large number of variables. Through assessing the significance of each variable, researchers select the appropriate model. Hence in social science applications, variable selection is an integrate part of mixed effect modeling. However, due to the large number of parameters, the traditional variable selection procedures, such as AIC and BIC, are computationally infeasible. Fan and Li (2001) proposed a class of variable selection procedures via nonconcave penalized likelihood (SCAD). The SCAD penalty has an Oracle property such that the estimators based on the SCAD penalty converge to the true model. The investigators propose to extend the ideas of Fan-Li and study the variable selection procedures via SCAD for linear and generalized linear mixed effect models. The work not only contributes to the estimation and computation of mixed effect models, but also adds to the theoretical understanding of them. The investigators plan to develop variable selection tools for applied researchers to simultaneously select variables and estimate parameters in the framework of mixed effect models.Measuring students' achievement and its determinants has been one of the central interests in educational research. In this area, data and research questions are usually hierarchical by nature. The typical data structure often seen in educational assessment is that students are nested within schools; sometimes more levels are involved, such as schools nested within geographical areas. It is important to address the impacts of different types of curriculums, availability of resources on individual student's academic performance, etc. For example, is a school's financial program important? Does school policy for parental involvement play a critical role regarding students' assessment? Such features of educational research have made hierarchical linear/generalized linear models the most important statistical tools in this field. Many such models start with a large array of explanatory variables (the National Assessment of Educational Progress (NAEP) has hundreds of variables at both teacher and school levels) and it is of particular interest for researchers to find the significant variables and estimate how important they are. The technique developed in this proposal will answer accurately which variables of teacher and school levels areimportant and to what degree they are so.

社会科学中的大多数研究问题都涉及个人行为与社会环境之间复杂的相互作用。为此，线性和广义线性混合效应模型得到了广泛的应用。混合模型的社会科学应用通常从大量变量开始。研究人员通过评估每个变量的显著性，选择合适的模型。因此，在社会科学应用中，变量选择是混合效应建模的重要组成部分。然而，由于参数数量众多，传统的变量选择程序，如AIC和BIC，在计算上是不可行的。Fan和Li（2001）提出了一类基于非凹惩罚似然（SCAD）的变量选择过程。SCAD惩罚具有一个Oracle属性，使得基于SCAD惩罚的估计器收敛到真实模型。研究者建议扩展范丽的思想，通过SCAD研究线性和广义线性混合效应模型的变量选择过程。该工作不仅有助于混合效应模型的估计和计算，而且增加了对混合效应模型的理论认识。研究人员计划开发变量选择工具，供应用研究人员在混合效应模型框架中同时选择变量和估计参数。衡量学生的成绩及其决定因素一直是教育研究的核心兴趣之一。在这个领域，数据和研究问题通常是分层的。在教育评估中经常看到的典型数据结构是学生嵌套在学校中；有时涉及更多的层次，例如在地理区域内嵌套的学校。重要的是要解决不同类型的课程的影响，资源的可用性对个别学生的学习成绩等。例如，学校的财务项目重要吗？学校有关家长参与的政策是否对学生的评估起到关键作用？教育研究的这些特点使得层次线性/广义线性模型成为该领域最重要的统计工具。许多这样的模型都是从大量的解释变量开始的（国家教育进步评估（NAEP）在教师和学校层面都有数百个变量），研究人员特别感兴趣的是找到重要的变量并估计它们的重要性。本提案中开发的技术将准确回答教师和学校水平的哪些变量是重要的，以及它们在多大程度上是重要的。