The World of Zero-Inflated Models, Volume 3: Using GLLVM

This is Volume 3 of the book series The World of Zero-Inflated Models, focusing on generalised linear latent variable models (GLLVMs). While volume 1 and volume 2 explored univariate response variables and their relationships with multiple covariates, this book dives into the analysis of datasets with multiple, correlated response variables. This volume continues the pagination and chapter numbering from volume 2, thus starting at page 495 with chapter 18.

GLLVMs are powerful tools for analyzing datasets where responses are inherently linked, enabling researchers to simultaneously model correlations and covariate effects. These models are described in detail by Niku et al. (2019), who provide efficient estimation approaches, and further extended by Van der Veen et al. (2023) with concurrent ordination techniques that integrate unconstrained and constrained latent variable modeling.

In ecological studies, for instance, datasets often include several response variables—species abundances, behavioural metrics, or environmental factors. Instead of reducing these variables to single metrics like species richness, GLLVMs allow you to model the correlations directly, uncovering shared patterns and underlying drivers. Through practical examples, this book showcases how GLLVMs can replace multiple univariate models and provide deeper insights into complex datasets.

This volume is ideal for researchers working with large ecological, biological, or environmental datasets with more than five response variables. Whether you’re studying species interactions, behavioural ecology, or environmental impacts, this book – guided by foundational work such as Niku et al. (2019) and Van der Veen et al. (2023) – will expand your analytical toolkit.

Multivariate Linear Mixed-Effects Models: When dealing with 2 to 5 correlated response variables, mixed-effects models with correlated random effects offer a structured approach. This book discusses how to implement these models, common optimisation issues, and when they may fail due to overfitting or model complexity.

Generalized Linear Latent Variable Models (GLLVMs): GLLVMs integrate GLMs/GLMMs with multivariate analysis techniques, allowing for the modeling of multiple response variables within a single framework. The book introduces key concepts, including count data models with many zeros, and explores distributions such as Poisson, negative binomial, zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and Tweedie. It also provides practical guidance on implementation in R using the gllvm package.

Advanced GLLVM Techniques: Beyond basic GLLVMs, the book introduces constrained GLLVMs, which extend the methodology through reduced-rank regression and redundancy analysis. It also covers concurrent ordination models, which integrate structured and unstructured latent variables, and applications for zero-inflated continuous data. Special attention is given to handling hierarchical structures through nested and crossed random effects.

Model Validation: A key component of this book is model validation, including diagnostic techniques such as checking residual patterns, assessing spatial and temporal dependencies, and using simulation-based validation methods like those provided in the DHARMa package. The book contrasts traditional diagnostic tools with modern, simulation-based approaches.

Target Audience: This book is suited for researchers, statisticians, and analysts working with multivariate ecological, environmental, or social science data. It is also a practical guide for R users looking to apply complex statistical models effectively.

Hands-on R Implementation: Each chapter includes detailed R code and case studies, demonstrating how to fit and interpret complex models, diagnose potential issues, and refine model performance. The book emphasizes practical solutions, helping readers apply these methods to real-world datasets.

Why This Book? Rather than presenting statistical models in isolation, this book explores their practical limitations and real-world performance. It provides a comprehensive introduction to mixed-effects and latent variable models, with an emphasis on hands-on application in R.