Advanced Generalized Linear Models: Correlated Data
Office hours by appointment
Erica E. M. Moodie
Purvis Hall room 38B
Phone: 398-5520 (email preferable: firstname.lastname@example.org)
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.
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)
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
Likelihood-based methods: Generalized linear mixed models
Semi-parametric methods: GEE, sandwich variance
Time-dependent covariates and marginal structural models
All course material is provided via myCourses.
Diggle, P.J., Heagerty, P.J, Liang, K.-Y. and Zeger, S.L. (2002). Analysis of
Longitudinal Data, Second Edition. Oxford University Press.
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
Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal
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).