Module 1: Classical methods (~ 1 day)

The first day revises basic statistical concepts and classical methods, and links them via the linear model and the generalised linear model.

• Lecture 1: Linear models

• Lecture 2: General linear models

[END OF DAY 1]

Module 2: Modelling with grouped non-independent data (~ 2.5 days)

The bulk of this course deals with the problem of non-independence of data and how to fix it appropriately using linear models. The main issue is recognizing how individual data points may be related to one another, which means that they share information. Our statistical tests assume that there is no relatedness between residuals generated by fitting models to the data. In this first section we deal with situations where that relatedness can be reasonably described by grouping related data points. This has the dual benefits of improving residual independence and also accounting for additional information in the data, potentially improving our test sensitivity. In doing this, we also recognise that accounting for this relatedness may not be essential to our questions; so we treat these additional model terms as random effects, and the predictors which are core to our questions we treat as fixed effects. Models with both fixed and random effects are called mixed effects models.

• Lecture 3: Intro to linear mixed models

• Lecture 4: LMM types

[END OF DAY 2]

• Lecture 5: Inference with LMMs

• Lecture 6: Predictions with LMMs

[END OF DAY 3]

• Lecture 7: GLMMs

[END OF DAY 4]

Module 3: Modelling with non-independent data that cannot be grouped (~1.5 days)

Certain types of data are non-independent, but the non-independence cannot be corrected by grouping, e.g. autocorrelation in spatial and temporal data, which depend on individual pairwise distances between points. In this module we introduce methods for dealing with non-independence between data points using correlation matrices.

• Lecture 8: Generalised least squares

• Lecture 9: Phylogenetic regression

• Lecture 10: Combining random effects and autocorrelation

Recognising that all data could contain both residual relatedness due to groups and due to pairwise relatedness means we need a model that can handle both situations.

The r code version we use here is based on Bayesian methods.

[END OF DAY 5]

If you have any questions about the course, please email:

XIA Xue (Course Coordinator): xiaxue@xtbg.org.cn, and/or

Kyle Tomlinson (Core Instructor): kyle.tomlinson@xtbg.org.cn