Mixed Linear Models

In this module we discuss how to analyse dependent data, that is, data for which the assumption of independence needed in Linear Models is violated. So: Do you have a nested experimental set-up? Like measurements on large plots, but also on smaller plots within the larger plots? Do you have repeated measurements? Like measurements on height of the same plant over time? Or weight of the same animal over time? Do you have pseudo-replication? Like measuring 3 plants from the same pot? In this sort of situations it is not reasonable to use ordinary ANOVA or regression to analyse your data. These methods are likely too optimistic, and you will get erroneous significant results. And your paper will be returned for, hopefully, a major revision! With mixed linear models a more appropriate model, allowing for dependence between observations, can be specified, which will lead to more reasonable conclusions.

In this module we will start with a refresher of the Linear Model (ANOVA, regression, ANCOVA), because it is the starting point of the Mixed Model. There will be attention for the matrix formulation of the Linear Model. After this we will gradually introduce the Mixed Model (also about the formulation in matrix notation, especially with respect to covariance matrices), the way to fit them to your data using software, and the output produced by the software. In computer sessions participants can practice fitting models of this type, and gain an understanding of the output created by the software. You are encouraged to bring along your own data if you have any. The main statistical software used in this course is R.

This course has been modified compared to previous years. The course Linear models has been integrated into this course and it is 3 days instead of 2. The evaluations of previous editions were included into consideration when the course was modified.