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This course will introduce mixed effect modelling from a Bayesian perspective. Mixed model is an unifying framework for analysing continuous, count, presence / absence and zero inflated data from environmental applications. We will explore the selection, interpretation and reporting of Bayesian mixed modelling results. The statistical programming language R and packages R-INLA, JAGS will be used in the labs and projects.
Chesapeake Biological Laboratory
Monday and Wednesday 11-12 p.m. IVN (TBD) Office hours: Wednesday 1–2:30 p.m.
Reference textbooks and website
- Cowles, M.K., Applied Bayesian Statistics, Springer
- Zurr, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., and Smith, G.M., Mixed Effects Models and Extensions in Ecology with R, Springer
- Rue, H. et al., www.r-inla.org
Grading and philosophy for the class
Grades will be based on a Pass and Fail system. Students are encouraged to carry out an independent project. They also have the option of leading the discussion of a peer reviewed paper.
There will be several lab sessions. Students are encouraged to apply the mixed effect modelling concepts and R tools to analyse published data sets.
There will be no exam in this class.
Discussion papers can be selected by students based on research interests. Please first consent the instructor. Discussion items will include understanding what the authors did, if or why a Bayesian approach was a good option, whether their choice of methods was appropriate, and whether you agree with the authors’ interpretation.
Students are encouraged to carry out individual project involving application of mixed effect models to problems of their own choosing by analyzing a real data set from their research. This might involve description of the research question and dataset, selecting an appropriate model, determining appropriate values for prior parameters, fitting the model using JAGS or R-INLA, checking convergence, and reporting and interpreting the results.
Projects will be carried out in three phases. Please consult with the instructor at least once while you are working on each phase.
- Project proposal is a short two paragraph description of what you plan to do, including question(s) to be addressed, dataset to be used, and methods to be applied.
- Project interim report is a five-pager, indicating that your project is on track. All computing should be done at this time. The report will include results obtained thus far and a brief summary (handwritten is OK) of what they mean and what remains to be done.
- Project presentation (presentation materials must be posted or submitted). Projects must be finalized in a form that can be shared with the entire class, such as posting a document on the course web page, preparing a poster, and giving an oral presentation with overheads, slides, or computer images. Posters and oral presentations will be given in class during the final week of classes.
Distribution of class materials
For the first several class periods, we will email reminders to get the info for class and where the info will be located. Please bookmark the Moodle site (https://moodle.cbl.umces.edu/login/index.php) in your web browser so that you can rapidly get there.
We will be using the distance learning tool, Moodle for storing and disseminating class information – class notes, computer code and output, assigned readings, and even discussion threads if you wish. Each student will be given a personal login and password to access the site. Materials for the next class will be posted no later than 12 hours before the beginning of the class. You are strongly encouraged to download and bring the R code and output to each class as these are critical components of the lectures and may be hard to follow without having these in front of you.
Spring Semester 2017 calendar
First day of classes - January 25 (Wednesday)
Spring Break - March 19-26 (Sunday-Sunday)
Project proposal - February 17 (Friday)
Project interim report - March 3 (Friday)
Last day of classes - March 15 (Wednesday)
Project presentation - March 13,15 (Monday and Wednesday)
Tentative Course Calendar
Topics - Reading
Review of linear regression - Zurr Appendix A
Linear mixed model and pseudo-replication - Zurr Ch 5
Linear mixed model and spatial correlation - Zurr Ch 7
Generalized linear model (GLM) - Zurr Ch 9
GLM and presence/absence data - Zurr Ch 10
GLM and zero inflated data - Zurr Ch 11
Generalized linear mixed model (GLMM) - Zurr Ch 16
GLMM and spatial data - Zurr Ch 21
Generalized additive mixed model (GAMM) and count data - Zurr Ch 21
GAMM and presence only data