Evaluating Independence in Linear and Generalized Linear Models

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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.