MATH48132 - 2007/2008

 

Specification

Aims

To study advanced techniques of statistical sciences, and to develop statistical skill of analyzing correlated data and cluster data. To explore a wide range of real-life examples occurring in particular in biology, medicine and social sciences.

Brief Description of the unit

In longitudinal studies, repeated measurements are made on subjects over time and responses within a subject are likely to be correlated, although responses between subjects may be independent. Data such as these are very common in practice, for example, in quality control in industry, panel data analysis in economics, growth curve analysis in biology and agriculture, randomized controlled trials in medical sciences, etc. When modelling such data without taking account of the correlation, statistical inferences can be very biased.

Learning Outcomes

On successful completion of this course unit students will have a good understanding of

• the principles and methods of longitudinal data analysis;
• the use of some standard statistical software (e.g., R or S-Plus) to analyze longitudinal data.

Future topics requiring this course unit

This course unit is naturally related to some other 4th year courses on statistical modelling, e.g., Linear and Generalized Linear Models, Survival Analsysis, etc.

Syllabus

1. Introduction: practical examples, longitudinal data exploration. [3 lectures]
2. General linear models for longitudinal data: typical covariance structures - compound symmetry and AR(1) structures, maximum likelihood estimates (MLE), restricted maximum likelihood estimates (REML). [7]
3. Growth curve models: models specification and parameter estimates including MLE and REML, hypothesis tests. [6]
4. Linear mixed models: random effects, variance components, MLE and REML, goodness of fit. [10]
5. Generalized linear mixed models: penalized quasi-likelihood (PQL) estimates, marginalized quasi-likelihood estimates, variance components estimates, goodness of fit [10]

Textbooks

• Davis, C. S., Statistical Methods for the Analysis of Repeated Measurements, Springer 2002.
• Diggle, P. J., Liang, K. Y. and Zeger, S. L., Analysis of Longitudinal Data, Oxford University Press 1994.
• Pan, J. and Fang, K. T., Growth Curve Models and Statistical Diagnostics, Springer 2002.

Teaching and learning methods

Three lectures and one examples class each week. In addition students should expect to spend at least six hours each week on private study for this course unit.

Assessment

 

End of semester examination: two and a half hours weighting 100%

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Arrangements