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I. Generalized linear models - Review regression and inference

Review of independent data with non-constant variance
Multinomial outcomes (POM, CRM)
Overdispersion
Approaches to inference - estimating functions (likelihood, quasi-likelihood,
empirical variance estimates)

II. GLM for correlated continuous data

Clustered data, longitudinal data (repeated measures)
Weighted least squares: maximum likelihood, REML, robust variance
Specification & estimation of the covariance matrix
Linear mixed models
Generalized Estimating Equations (GEE)

III. GLM for correlated categorical data

Longitudinal data (repeated measures)
Clustered/multi-level data
Multivariate responses
Spatial data
Semi-parametric methods: GEE, sandwich variance
Likelihood-based methods: GLMM

** CLASS NOTES are available on WebCT **

EPIB 612 - Fall 2010 Advanced Generalized Linear Models: Correlated Data (4 credits; Fri 10:00am-12:00pm + discussion/lab; 12:00-1:00pm Purvis Hall 24) Office hours by appointment Erica E. M. Moodie Purvis Hall room 38B Phone: 398-5520 (email preferable: first.last@mcgill.ca)
Prerequisite:	MATH 523 or equivalent.
Objectives:	This aim of this course is to extend linear model methods for analysis of data with mean-variance relationships and data with non-iid errors. The class will highlight common features of tools for analysis of correlated data with a focus on longitudinal data, and to give a general approach to the analysis of these data.
Content:	This course will have theoretical content but will focus on applications. Students can use any statistical software they wish; the R software package will be used for in-class illustrations. R is available (free) at http://lib.stat.cmu.edu/R/CRAN. Topics to be covered are: I. Generalized linear models - Review regression and inference Review of independent data with non-constant variance Multinomial outcomes (POM, CRM) Overdispersion Approaches to inference - estimating functions (likelihood, quasi-likelihood, empirical variance estimates) II. GLM for correlated continuous data Clustered data, longitudinal data (repeated measures) Weighted least squares: maximum likelihood, REML, robust variance Specification & estimation of the covariance matrix Linear mixed models Generalized Estimating Equations (GEE) III. GLM for correlated categorical data Longitudinal data (repeated measures) Clustered/multi-level data Multivariate responses Spatial data Semi-parametric methods: GEE, sandwich variance Likelihood-based methods: GLMM CLASS NOTES are available on WebCT
Texts:	Required text: Diggle, P.J., Heagerty, P.J, Liang, K.-Y. and Zeger, S.L. (2002). Analysis of Longitudinal Data, Second Edition. Oxford University Press. Additional resource: Collett, D. (2003) Modelling Binary Data, Second Edition. Chapman & Hall In particular: chapters 3, 6-8 and section 10.1 Fitzmaurice, G.M., Laird, N.M. and Ware, J.H. (2004). Applied Longitudinal Analysis, Wiley. Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer-Verlag.
Evaluation:	Assignments (~6) 25% In-class presentations/discussion 25% Take-home final exam (1 week) 50%

Note on academic integrity: McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/integrity/ for more information).
ASSIGNMENTS AND SOLUTIONS