Description
Longitudinal data, which refer to the data collected over time on multiple subjects or people, are frequently observed in medical, economical, behavioural and pharmaceutical studies. Two main challenges in the analysis of longitudinal data are that the repeated measurements on the same subject are correlated and there is often a high variability and heterogeneity between subjects or patients to be taken into account in the statistical analysis (see the examples in the figures to the right). Mixed-effects models, which are a class of advanced regression models, are well suited for the analysis of longitudinal data where they allow us to effectively study the changes over time and to understand how the changes vary across different people or groups. Mixed-effects models are therefore commonly applied by researchers and practitioners, for example, in medicine (e.g., to study the treatment effects over time), social science (e.g., to study the people/children behaviour over time), finance (e.g., to study stock price over time), and insurance (e.g., to predict the insurance risk and costumers claims), to name but a few.In this project, the student will first study the theory and algorithms of mixed-effects models by focusing on linear or generalised linear mixed-effects models, and then apply these models to real-world data sets. The statistical analyses can be done either in R or SAS (preferably R), providing the opportunity for the student to gain practical experience with real data analysis and develop computational skills. Depending on the student interests, the project could be theoretical or applied, or a combination of both.
Prerequisites
- Statistical Methods III
Resources
- Verbeke, G. and Molenberghs, G. (2000). Linear mixed models for longitudinal data. Berlin: Springer.
- Molenberghs, G. and Verbeke, G. (2006). Models for discrete longitudinal data. Springer Science & Business Media.
- Demidenko, E. (2004). Mixed Models: Theory and Applications. New York: Wiley.
- Rao, K., Drikvandi, R. and Saville, B. (2019). Permutation and Bayesian tests for testing random effects in linear mixedâeffects models. Statistics in Medicine 38, 5034-5047.
