10-13 June 2024

Multivariate analysis of ecological communities is often performed with a set of loosely connected methods that rely on distance measures (e.g., C(C)A, NMDS, PCoA). In the last decade, Generalized Linear Latent Variable Models (GLLVMs) have been proposed as an alternative, unifying framework, for performing ordination, and for jointly analysing the occurrence patterns of multiple species. GLLVMs can be considered as a multivariate extension of GL(M)Ms, so that they inherit many of the useful properties of both GLMs and of ordination methods. However, the explicit statistical model formulation makes GLLVMs more flexible than classical ordination methods, and provide many useful tools for inference and for performing diagnostics.

The course is aimed at PhD candidates, postdoctoral researchers and researchers with basic statistical knowledge, that have multivariate data (which can be experimental or observational) and want to learn how to analyse it in a statistically appropriate manner. Familiarity with concepts in generalised linear models (e.g., distribution, link function, mean-variance relationship, uncertainty quantification) for different response types, generalised linear mixed models (e.g., variance parameters, quirks that come with mixed models) in the lme4-sense, or classical ordination techniques (e.g., biplots, latent variables), is an advantage. Basic knowledge in the R programming language is required.

•     Fitting GLLVMs with the gllvm R-package, choosing the appropriate distribution for data.

•     Formulating an appropriate GLLVM to answer a research question.

•     Finding a "good" GLLVMs based on residual diagnostics and other criteria covered in the course.

•     Visualizing and interpreting results from a fitted GLLVM.

•     The ability to effectively communicate the results.

Monday – Classes from 2-8 PM Berlin time

Recap of related methods including generalised linear models, generalised linear mixed models, and concepts in classical multivariate analysis (i.e., ordination).
Introduction to the gllvm R-package.


Tuesday – Classes from 2-8 PM Berlin time

Background on GLLVMs with ecological examples.
Introduction to ecological gradient theory: what are latent variables?
Species co-occurrence patterns: Joint Species Distribution Models or ordination?
Benefits of GLLVMs over classical ordination methods, with practical demonstration.


Wednesday – Classes from 2-8 PM Berlin time

Fitting an ordination with covariates.
Model checking and selection.
Some suggestions on visualizing results, drawing inference from GLLVMs.


Thursday– Classes from 2-8 PM Berlin time

Going beyond vanilla GLLVMs: a brief look at hierarchical ordination and other hierarchical GLLVMs.
Opportunity for fitting GLLVMs to your own data.