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Evaluating Independence in Linear and Generalized Linear Models

评估线性和广义线性模型中的独立性

基本信息

批准号：
9625897
负责人：
Ronald Christensen
金额：
$ 6万
依托单位：
University of New Mexico
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1996
资助国家：
美国
起止时间：
1996-07-01 至 1998-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625897&HistoricalAwards=false
关键词：
Evaluating Independence Linear Generalized Models

项目摘要

DMS 96-25897 Christensen The investigators study methods for evaluating the independence assumption in standard normal theory linear models and in generalized linear models. The research develops both formal tests and informal graphical procedures for evaluating independence. The methods are based on the formation of rational subgroups of observations that were collected under similar circumstances. The formal tests for independence are based on models that incorporate the subgroups into the linear structure. For normal theory linear models the procedures can also be used to provide tests for variance component models. The researchers study the properties of these tests. Statistical models are widely used in the physical and social sciences for prediction and for understanding the relationships among factors in complex systems. Statistical models are used in environmental evaluation, to improve industrial processes, and to develop chemical processes. An important assumption made in most statistical models is that observations are obtained ``independently'' of one another. This assumption has important ramifications for the validity of statistical procedures. Assuming independence, when it is not true, can lead to erroneous conclusions. Unfortunately, this assumption has traditionally been very difficult to evalute. The investigators develop new methods for evaluating the validity of the independence assumption and study the behavior of those methods.

DMS96-25897克里斯滕森，研究人员研究在标准正态理论线性模型和广义线性模型中评估独立性假设的方法。这项研究开发了用于评估独立性的正式测试和非正式图形程序。这些方法的基础是形成在类似情况下收集的观察数据的合理分组。正式的独立性测试是基于将子群合并到线性结构中的模型。对于正态理论线性模型，该程序也可用于提供方差分量模型的检验。研究人员研究了这些测试的特性。统计模型在自然科学和社会科学中被广泛用于预测和理解复杂系统中各因素之间的关系。统计模型被用于环境评价、改进工业过程和发展化学过程。在大多数统计模型中作出的一个重要假设是，观测数据是彼此“独立”获得的。这一假设对统计程序的有效性有重要影响。假设独立，而事实并非如此，可能会导致错误的结论。不幸的是，这一假设传统上很难评估。研究人员开发了新的方法来评估独立性假设的有效性，并研究了这些方法的行为。