This is Volume 2 of our book series 'The World of Zero-Inflated Models'. In Volume 1, we used datasets for which ordinary generalised linear models (GLM) and zero-inflated models were sufficient. In this volume, we increase the complexity of the datasets and models by allowing for a dependency structure. We do this 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.
Writing this volume took longer than anticipated. Volume 1 was published in 2021, and then the aftermath of the pandemic kicked in. We had to convert all our courses to online and on-demand formats, which took some time. In 2023, we had to convert everything back to onsite and hybrid courses. We used the material from this book in various online courses, which turned out to be an excellent peer-reviewing process. Then there was (and still is) the delightful chaos caused by the first author’s two young children. They require a generous amount of pleasant attention. Finally, there is our own writing ambition. Just when we thought the book was complete, we discovered that the glmmTMB package had introduced the ordered beta distribution for analysing proportional data with zeros and ones. Naturally, we felt compelled to include this exciting development.
We also stumbled upon a paper by van der Veen et al. (2023), extending the work of Niku et al. (2019), discussing generalised linear latent variables (GLLVM). If you sample multiple species at the same site, it is convenient to convert this into a univariate diversity index and apply a GLM or a GLMM (with or without zero-inflation components). However, a GLLVM is a multivariate GLMM that allows for the analysis of the individual species in a multivariate framework. A GLLVM can be fitted with the gllvm function from the gllvm package, which also allows for zero-inflated Poisson, zero-inflated negative binomial, Tweedie, and ordered beta distributions. Hence, we immediately wrote another 150 pages on GLLVMs and applied them to zero-inflated data. However, this made the book excessively long—too large to fit through a letterbox (even a generously sized one).
Therefore, we decided to split the material. This volume covers univariate GLMMs, and we will simultaneously release Volume 3, focusing on GLLVM. This was not our original plan, as we intended to include zero-inflated GAMMs in Volume 3. These will now appear in Volume IV. Who knew the world of zero-inflated data could expand faster than our to-do list?
So, what is in this book?
Chapter 11 contains an extensive explanation of linear mixed-effects models. Originally, we used a dataset of bears and ants, but after discovering that the covariates only explained 2% of the variation, we decided to completely rewrite this chapter with a different dataset on painted turtles. At that point, we had forgotten that the chapter on zero-inflated binomial GLMMs also uses painted turtle data. So, we hope you like turtles.
In Chapter 12, we first introduce Poisson GLMM using a squirrel dataset and discuss marginal and conditional predicted values. The chapter also covers zero-inflated Poisson and generalised Poisson GLMMs. A zero-inflated Poisson GLMM is applied to a humphead fisheries dataset in Chapter 13. In Chapter 14, we discuss how to handle nested and crossed random effects, as well as auto-correlation, using a dataset on zero-inflated tree hyrax count data.
A detailed explanation of zero-inflated binomial GLMMs is provided in Chapter 15. We use a dataset on painted turtles and also touch upon beta-binomial models. In contrast, 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 Chap17 presents an application of the Tweedie GLMM to zero-inflated biomass data.
The Preface of this book outlines how to access the R code and data sets used in this volume. For a detailed description, table of contents, R code and data sets, click here.
References
Niku, J., Brooks, W., Herliansyah, R., Hui, F. K. C., Taskinen, S., and Warton, D. I. (2019). Efficient estimation of generalized linear latent variable models. PLOS ONE, 14(5):e0216129. Publisher: Public Library of Science.
van der Veen, B., Hui, F. K. C., Hovstad, K. A., and O’Hara, R. B. (2023). Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling. Methods in Ecology and Evolution, 14(2):683–695. _-eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.14035.