Generalised Additive Models for the analysis of spatial and spatial-temporal data

This online course consists of 4 modules representing a total of approximately 36 hours of work. We will start with a non-technical introduction to generalised additive models (GAM). Using a series of exercises, we show how GAMs can be used to allow for non-linear covariate effects. Once we are familiar with GAM, we will apply them to various spatial, and spatial-temporal data sets.

During the course, GAMs are applied to count data, absence-presence data, proportional data, and continuous data using the Gaussian, Poisson, negative binomial, Bernoulli, beta, gamma and Tweedie distributions. We will apply GAMs with 2-dimensional smoothers to analyse spatial data. To allow for natural barriers (e.g. an island in the sea), soap-film smoothers are used. On the 4th day of the course, spatial-temporal data sets are analysed.

The course contains a short revision of generalised linear models (GLM). During the course, we will explain the beta, Gamma, and Tweedie distributions. Preparation material on data exploration and linear regression with on-demand video is supplied. Throughout the course we will use the mgcv package in R. This is a non-technical, and easy-to-follow course.

The course website contains the following modules.

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 GAM.
• Three introductory GAM exercises.
• Key phrases: How to fit a GAM using mgcv, how to read its output, model selection, model validation,
smoother interactions, what to present in a paper.

Module 2

• Revision of Poisson and negative binomial GLM.
• Two revision exercises on Poisson and negative binomial GLM.
• One exercise on negative binomial GAM.
• Two exercises on GAMs applied to spatial data

Module 3

• Catching up.
• Two exercises showing how to use GAM with a spatial smoother in case the study area contains a natural
barrier (e.g. an island in the sea).
• Time allowing: GAM applied to areal data.
• Time allowing: GAM applied to data measured on a sphere.

Module 4

• Four exercises GAM applied to spatial-temporal data using a variety of distributions (e.g. Poisson, negative
binomial, Bernoulli, Tweedie, Gamma, beta).

The course material consists of relevant pdf files of presentations, data sets, and clearly documented R code.
Course participants will be given access to the course website with all data sets, R solution code, and course material 2 weeks before the start of the course.

PRE-REQUIRED KNOWLEDGE:
Working knowledge of R and linear regression. This is a non-technical course.