EPIB 612

Advanced Generalized Linear Models: Correlated Data

 4 credits

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
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.





Some tips on report-writing, and some useful references on common errors in analysis and reporting: Altman (1998) Stats in Med 17: 2661-2674, Strasak et al (2007) Swiss Med Wkly 137:44-49, Bacchetti notes.
Some handy code and an example for creating LaTeX code for a descriptive table in R, courtesy of a previous student (Ben Rich).