Introduction GLMs with spatial correlation and GLMM. A Bayesian’s perspective using R-INLA

This is an onsite course, but you can also participate online via a Zoom connection

This course introduces spatial generalised linear models (GLMs) and generalised linear mixed-effects models (GLMMs) using R-INLA, with a strong focus on Bayesian approaches tailored for biological and ecological research.

We begin by adding spatial dependency to regression models with frequentist tools, exploring their limitations before moving to Bayesian techniques that better capture complex natural processes. In the second part, we address hierarchical data, enabling analysis of multiple observations from the same animal, site, or ecosystem unit. With hands-on examples in R-INLA, participants will gain practical skills to model ecological and biological data, including spatial patterns and dependencies vital to environmental and field research.

Pre-required knowledge: Working knowledge of R, data exploration, linear regression and GLM (Poisson, negative binomial). This is a non-technical course. The course website provides preparatory materials, including on-demand videos and R scripts covering multiple linear regression, basic matrix notation, generalised linear models, model validation using DHARMa, and the explanation of variograms. If you are not familiar with these methods, please review them before the course begins.

1 hour face-to-face: The course includes a 1-hour face-to-face video chat with the instructors (to be used after the course). You are invited to apply the statistical techniques discussed during the course on your own data and if you encounter any problems, you can ask questions during the 1-hour face-to-face chat.

A discussion board (access for 12 months) allows for interaction on course content between instructors and participants.

Course content:

Preparation material (containing on-demand video):

  • Revision exercise on multiple linear regression.
  • Introduction to matrix notation.
  • Introduction to DHARMa.
  • What is a variogram.

Module 1:

  • General introduction.
  • Theory presentation on adding temporal dependency, and spatial dependency to a regression model using frequentist techniques.
  • One exercise showing how to add spatial dependency to a regression model using frequentist tools.
  • Brief introduction to Bayesian analysis.
  • Conjugate priors.
  • Diffuse versus informative priors

Module 2:

  • Theory presentation on INLA.
  • Exercise showing how to execute a linear regression model in R-INLA.
  • Theory presentation on adding spatial correlation to a regression model using in R-INLA.
  • Exercise showing how to add spatial correlation to a linear regression model.

Module 3:

  • Exercise showing how to execute a Poisson GLM in R-INLA.
  • Exercise showing how to add spatial correlation to a Poisson GLM.
  • Exercise showing how to add spatial correlation to a negative binomial GLM.
  • Time allowing: Exercise showing how to add spatial correlation to a Bernoulli GLM.

Module 4:

  • Linear Mixed-Effects Models for Hierarchical Data
  • Theory: Linear mixed-effects models for nested data structures.
  • Two exercises: Linear mixed-effects models with random intercepts in R-INLA.

Module 5:

  • Generalised Linear Mixed Models (GLMMs)
  • Exercise: Poisson GLMM for count data analysis.
  • Exercise: Negative binomial GLMM for count data analysis.
  • Exercise: Negative binomial GLMM with nested and crossed random effects.
  • Time allowing: Exercise: Bernoulli GLMM

We reserve the right to change the exercises. Pdf files of all theory material will be provided. All exercises consist of data sets and annotated R scripts. Access to the course website is for 12 months.