Theories of Hierarchical and Other Richly
Parametrized Linear Models
Course Syllabus Spring 2010
Moos Health Sci Tower 2-116
James S. Hodges, Assoc Prof, Div of Biostat
University Office Plaza, 2221 University Ave SE, Suite 200
By arrangement with individual students
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.
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).
first purpose of this collection is to illustrate the range of difficulties that a theory should explain, predict, and, if
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.
present their projects in class and hand in a written version.