The framework of (generalised) linear mixed models (GLMMs) is the de facto standard for the statistical analysis of experimental and observational data. The GLMM framework extends standard LM/GLM models with a) random effects to account for grouped data, b) variance structures to account for non-constant variances (heteroscedasticity), and c) correlation structures to account for residual spatial, temporal, and phylogenetic autocorrelation. In this course you will learn to specify, interpret, and validate linear and generalized linear mixed models. The focus is on producing a valid and defensible analysis of experimental or observational data in an applied research context in R, with an emphasis on the lme4 and glmmTMB regression packages.

This course is aimed at graduate students and researchers who have experience with generalized linear regression models in R and want to extend their knowledge by learning how to add random effects, correlation structures, and variance models (to account for heteroscedasticity) to these models. The basics of LM, GLM, and ANOVA are reviewed at the beginning of the course, but if you do not have a solid understanding of these topics, you would probably benefit more from the course "Generalized Linear Models as a unified framework for data analysis in R", which is also offered by Physalia.

1. Deepen your understanding of fundamental regression concepts, including centering, scaling, interactions, contrasts, and ANOVA.
 
2. Understand the components of the GLMM framework (choice of distributions, random effects, variance structures, correlation structures)
 
3. Being able to choose the appropriate model structure in an applied analysis of experimental or observational data (focusing on the R packages lme4 and glmmTMB)

4. Being able to interpret the fitted models and calculate the expected effect of predictors on the response.
 
5. Know how to visualize fitted GLMMs (R package effects) and to check the assumptions of the model (R package DHARMa)

Sessions from 14:00 to 20:00 (Monday to Thursday), 14:00 to 18:00 on Friday (Berlin time).  Sessions will be a mix of lectures, in-class discussion/ Q&A, and practical exercises over Slack and Zoom.

Monday– Classes from 2-8 PM Berlin time

On day 1, we will recap regression basics that would typically be covered in an introductory stats course: 1) the linear model: interpretation, diagnostics, multiple regression, scaling and centering, omitted-variable bias, interactions 2) contrasts for categorical predictors 3) ANOVA


Tuesday– Classes from 2-8 PM Berlin time

On day 2, we will introduce random effects and variance structures (GLS), and talk about model selection and causal inference.

Wednesday– Classes from 2-8 PM Berlin time

On day 3, we will merge the topics from day 2 (variance structures and random effects) with the GLM framework, which means that we arrive at using GLMMs. We will talk about specification, diagnostics, and common issues when working with GLMMs, in particular variance partitioning and model selection for fixed and random effects. If we have time, we will also introduce cross-validation and the bootstrap.


Thursday– Classes from 2-8 PM Berlin time

Day 4 is about correlation structure in the data, other than random effects. Specifically, we'll talk about spatial, temporal and phylogenetic correlation structures and how to account for them in regression models.


Friday– Classes from 2-6 PM Berlin time

On day 5, we will speak about some advanced topics, in particular non-parametric methods, including null models, the boostrap and cross-validation, and how they relate to parametric methods, Bayesian estimation vs. frequentist estimation of GLMMs, or structural equation models. Emphasis can be changed depending on the interest of the group.

Should you have any further questions, please send an email to info@physalia-courses.org