Official_Syllabus_PUBH8400-1_Spr_2010

Official_Syllabus_PUBH8400-1_Spr_2010 - PubH 8400-001...

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PubH 8400-001 Theories of Hierarchical and Other Richly Parametrized Linear Models Course Syllabus Spring 2010 Credits: 3 Meeting Days: T/Th Meeting Time: 4:00pm-5:15pm Meeting Place: Moos Health Sci Tower 2-116 Instructor: James S. Hodges, Assoc Prof, Div of Biostat Office Address: University Office Plaza, 2221 University Ave SE, Suite 200 Office Phone: 612-626-9626 Fax: 612-626-9054 E-mail: hodge003@umn.edu Office Hours: By arrangement with individual students I. Course Description Linear richly-parameterized models include hierarchical models, hierarchical generalized linear models, dynamic linear models (Kalman filters), linear mixed models, random regressions, smoothers (including spatial or spatiotemporal smoothers), longitudinal models, and others too numerous to mention. Such theory as exists is mainly schemes for specifying and fitting large classes of models. The most ambitious schemes are based on mixed linear models (Ruppert, Wand & Carroll 2003), Gaussian Markov Random Fields (Rue & Held 2005), and the so-called h-likelihood (Lee, Nelder & Pawitan 2006). The first part of this course describes the scheme based on mixed linear models, gives the standard theory (conventional and Bayesian) and discusses computing. The other two schemes will be discussed briefly as contrasts and to illustrate some of their advantages compared to mixed linear models. There is, as yet, no well-developed theory of richly-parameterized models analogous to the beautiful, powerful theory of ordinary (single error term) linear models. The second part of this course begins with the little theory that exists and the rest of the semester considers odd, surprising, or undesirable results that the instructor and his students have stumbled on while analyzing datasets from collaborative research projects (i.e., real datasets). The first purpose of this collection is to illustrate the range of difficulties that a theory should explain, predict, and, if possible, avoid. The second purpose is to serve as starting points for such a theory. This part of the course draws largely on work by the instructor and his colleagues and students, mostly using the mixed-linear-model scheme, and will point out cavernous gaps in our knowledge suitable for doctoral dissertations. The course consists mainly of lectures. The grade depends on some homework exercises but largely on a class project, the steps of which (selecting a topic, etc.) are given as homework exercises, to help students avoid putting off their projects until the end of the semester. The project can a piece of theory, a simulation experiment, a literature review, or another type of project mutually agreeable to the instructor and student. Students will present their projects in class and hand in a written version. II.
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Official_Syllabus_PUBH8400-1_Spr_2010 - PubH 8400-001...

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