Proposal: DMS 95-05065 PI: Elizabeth Slate, 1991 Institution: Cornell University Title: Reparameterization and Longitudinal Modeling Abstract: This research is concentrated in two main areas of statistical inference and modeling: reparameterization and hierarchical models for longitudinal data. The reparameterization research develops methodology that identifies parameterizations for a wide class of statistical models for which normal approximations to the likelihood function and posterior density are accurate. Parameterization diagnostics based on measures of non-normality are used to identify well-behaved parameterizations and to derive sample sizes sufficient for reliable inference based on asymptotic normality for many commonly-used parameterizations. The hierarchical modeling component of the research compares and unifies models for longitudinal data, including Markov chain models, hierarchical mixed effects models, and fully Bayesian hierarchical models. Estimation, prediction and design issues are addressed, and special consideration is given to the incorporation of random changepoints in these models. This research studies statistical models which may be uqed for processes such as the basis of a feed-forward controller for many of today's complex manufacturing processes. Because exact inference can be very difficult in these complicated models, scientists often resort to the simplification of summary results which are implicitly understood in the context of normality (i.e., the bell curve). The first component of this research studies procedures for determining when this simplification is misleading and presents alternative statistical models. This research will lead to increased numerical efficiency in fitting these complex models, permitting more timely response to changing processes. The second component of this research studies models for longitudinal data. These models are needed when the data consist of serial mea surements within individuals for a number of individuals. Such data arise in a wide range of applications, from reliability studies to economic indicators to health monitoring. The research compares and unifies a number of models for longitudinal data, and addresses estimation, prediction and design issues. Special consideration is given to the incorporation of random changepoints in these models (i.e., points in time where the process exhibits some serious change in behavior). The changepoints may represent onset of disease, critical part fatigue, or changes in consumer behavior. The research studies how longitudinal models may be used in a dynamic fashion to detect these changepoints quickly.
