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This is Volume 3 of the book series The World of Zero-Inflated Models. The central theme of this book is the multivariate extensions of generalised linear models (GLM) and generalised linear mixed-effects models (GLMM). Although this book is published under the umbrella of The World of Zero-Inflated Models, it also provides a good introduction to ordinary multivariate GLMM and GLLVM. It is published simultaneously with volume 2, which covers generalised linear mixed effects models (GLMMs) with dependency structures. The planned treatment of zero-inflated GAMMs is deferred to volume 4.
In volume 1 and volume 2, the authors analysed univariate response variables as a function of multiple covariates. In most chapters, the original datasets consisted of multiple response variables that were typically converted into a diversity index, such as species richness or total abundance, or put aside with the analyses focusing on one specific species or variable. However, in most of these datasets, the response variables are correlated. There are several reasons why response variables might be correlated beyond direct cause-effect relationships or mutually exclusive activities. Additional biologically relevant reasons can include:
- Shared underlying factors: Different response variables might be influenced by the same underlying environmental or biological factors. For instance, both feeding time and vigilance in caribou could be influenced by the availability of food and the presence of predators.
- Temporal or spatial proximity: Variables might be correlated due to occurring at the same time or in the same location. For example, if certain behaviours tend to happen during specific times of the day, variables measured during those times might show correlation.
- Biological constraints: Organisms often face biological limitations that cause correlations between different traits or behaviours. For instance, physiological needs might limit how much time an animal can spend on certain activities, creating correlations between them.
- Behavioural syndromes: Animals might exhibit consistent behaviour patterns across different contexts, known as behavioural syndromes. For example, an animal that is generally more active might spend more time both walking and feeding, leading to a positive correlation between these activities.
- Environmental conditions: Correlation can arise due to shared responses to environmental conditions. For example, during harsh weather, an animal might reduce overall activity, affecting multiple behaviours similarly.
Instead of applying multiple univariate GLMMs, this book discusses multivariate GLMMs for datasets with a relatively small number of response variables and generalised linear latent variable models (GLLVMs) for datasets with a relatively large number of response variables.
This volume continues the pagination and chapter numbering from volume 2, thus starting with chapter 18.
