GLMs and GAMs with Spatial, Temporal, or Spatial-Temporal Correlation using INLA

 

Live online, onsite or self-study course

 

GLMs and GAMs with Spatial, Temporal or Spatial-Temporal Correlation using INLA

 

This course offers a practical introduction to the analysis of spatial, temporal, and spatial-temporal data using generalised linear models (GLMs) and generalised additive models (GAMs) in R-INLA. We begin with how to add spatial structure to regression models using frequentist techniques, and then introduce Bayesian methods, focusing on how to implement models with spatial and temporal dependency using INLA. The course covers a range of data types and distributions, including Gaussian, Poisson, generalised Poisson, negative binomial, Bernoulli, and Tweedie.

Participants will learn how to build models that incorporate spatial correlation, temporal trends, and spatio-temporal structure, and how to address practical challenges such as modelling in the presence of natural barriers (e.g., coastlines, forests) that prevent spatial correlation from extending freely across space, such as marine/terrestrial boundaries or fragmented habitats. We will also cover the use of more complex spatial meshes and multivariate likelihoods to accommodate study areas with isolated groups of sites.
We will utilise the R package inlabru.

Through hands-on exercises, you will gain experience in fitting and interpreting models for continuous, count, and binary data, and understand how to adapt your models to the specific structure and distribution of your data. This is an applied and non-technical course that focuses on the practical implementation in R.

Course content

Module 1

  • General introduction.
  • Theory presentation 1: Adding temporal dependency, or spatial dependency to a regression model using frequentist techniques.
  • Exercise 1: Adding temporal correlation to a regression model.
  • Exercise 2: Linear regression model with spatial correlation applied to the Irish pH data using sdmTMB.
  • Theory presentation 2: Brief introduction to Bayesian analysis and INLA. Conjugate priors, and diffuse versus informative priors.
  • Bonus Exercise 3: Linear regression with spatial correlation applied to the snake data using sdmTMB.

Module 2

  • Exercise 4: Linear regression model without spatial correlation applied to the Irish pH data using inlabru.
  • Theory presentation 3: Adding spatial correlation to a regression model using in INLA.
  • Exercise 5: Linear regression model with spatial dependence applied to the Irish pH data using inlabru.
  • Bonus Exercise 6: Linear regression with, and without spatial dependence applied to the snake data.
  • Exercise 7: Executing a Poisson GLM in R-INLA using the La Palma data.

Module 3

  • Exercise 8: Adding spatial correlation to a Poisson GLM using the La Palma data.
  • Exercise 9: Fitting a negative binomial GLM with spatial dependency to the Belgium butterfly data.
  • Exercise 10: Bernoulli GLM with spatial dependence applied to the skates data.
  • Exercise 11: Barrier model applied to the Samoa coral reef data.
  • Theory presentation 4: Time series analysis - With GAM as a bonus -

Module 4

  • Catching up.
  • Exercise 12: Applying a GAM to the Norwegian squid data using inlabru.
  • Exercise 13: Time series analysis of the Assyrian core data.
  • Exercise 14: Hierarchical time series analysis using the snow data.
  • Exercise 15: GAM with spatial dependence and multiple likelihoods using the polar bear data.
  • Exercise 16: GAM with a temporal trend and spatial dependence using the Irish Marsh Fritallary butterfly data.

Module 5

  • Theory presentation 5: Spatial-temporal correlation using the replicate and auto-regressive (AR1) correlation.
  • Exercise 17: Spatial-temporal Poisson and negative binomial GLM applied to the Canadian owl data.
  • Exercise 18: Spatial-temporal Tweedie GLM applied to the Eulachon data.
  • Exercise 19: Spatial-temporal Bernoulli GLM applied to the coral disease data.

We reserve the right to change the exercises. Pdf files of all theory material will be provided. All exercises consists of data sets and annotated R scripts. Access to the course website is for 12 months. The course website also contains on demand video.

Pre-required knowledge
Working knowledge of R, data exploration, linear regression and GLM (Poisson, negative binomial, Bernoulli). 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.

General
Please ensure that you have system administration rights to install R, and R packages on your computer.  Instructions what to install is on the course website.