Evaluating Independence in Linear and Generalized Linear Models

研究者研究了标准正态理论线性模型和广义线性模型中独立性假设的评价方法。研究开发了正式的测试和非正式的图形程序来评估独立性。这些方法是基于在类似情况下收集的观察结果的合理子组的形成。独立性的正式测试基于将子组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成分模型的检验。研究人员研究了这些测试的特性。统计模型在物理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。统计模型用于环境评价、改进工业流程和开发化学流程。大多数统计模型的一个重要假设是，观测结果是彼此“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，当它不是真的，可以导致错误的结论。不幸的是，这个假设传统上很难评估。研究者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。

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.