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This is Volume 2 of the book series The World of Zero-Inflated Models. In Volume 1, the authors used datasets for which ordinary generalised linear models (GLM) and zero-inflated models were sufficient. In this volume, they increase the complexity of the datasets and models by allowing for a dependency structure. This is done via random effects in generalised linear mixed effects models (GLMMs). Although this book is published under the umbrella of The World of Zero-Inflated Models, it also provides a good introduction to ordinary linear mixed-effects models and GLMMs.
Due to the pandemic and its aftermath, writing this book took longer than expected. Furthermore, the authors wanted to include the latest developments. First, this includes the release of the glmmTMB package, which introduces the ordered beta distribution for analysing proportional data with zeros and ones. The second development, generalized linear latent variable models (GLLVMs), added so much material that this will be published separately and simultaneously in volume 3. The planned treatment of zero-inflated GAMMs is deferred to volume 4.
This volume continues the pagination and chapter numbering from volume 1, thus starting at page 279 with chapter 11. Chapter 11 contains an extensive explanation of linear mixed-effects models using a dataset on painted turtles. Chapter 12 introduces Poisson GLMMs using a squirrel dataset and discusses marginal and conditional predicted values. The chapter also covers zero-inflated Poisson and generalised Poisson GLMMs. Chapter 13 applies a zero-inflated Poisson GLMM to a humphead fisheries dataset. In Chapter 14, the authors discuss how to handle nested and crossed random effects, as well as auto-correlation, using a dataset on zero-inflated tree hyrax count data. Chapter 15 provides a detailed explanation of zero-inflated binomial GLMMs, again using a dataset on painted turtles, and also touches on beta-binomial models. Chapter 16 utilises beta GLMMs, zero-inflated beta GLMMs, zero-altered beta GLMMs, and ordered beta GLMMs for the analysis of zero-inflated caribou data. Finally, Chapter 17 presents an application of the Tweedie GLMM to zero-inflated biomass data.
