The World of Zero-Inflated Models, Volume 1: Using GLM

This is the first of four volumes that introduces the reader to the world of zero-inflated models. It discusses models for count data and continuous data with an excessive number of zeros. All models are extensions of generalised linear models (GLMs). In volume 2, count data, continuous data and proportional data using GLMMs are analysed. This extends the models from volume 1 with random intercepts and random slopes. Volume 3 carried very recent developments in generalized linear latent variable models (GLLVMs). In volume 4, the models from volumes 1-3 are extended towards GAMs and GAMMs. Volume 1 can be read as a stand-alone. Volume 2 assumes that you have read volume 1, and volume 4 is a continuation of volumes 2 and 3.

The world of zero-inflated models is large and complex. The first layer of complexity is the type of data. The three books in this series analyse count data, continuous data, proportional data, density data, etc.

The second layer of complexity is that, for each of these data types, there are multiple options for choosing a statistical distribution. For count data, the book discusses the Poisson, negative binomial (NB), generalised Poisson (GP) and Conway–Maxwell–Poisson (CMP) distributions. For continuous data, the book applies the Tweedie distribution and the zero-altered Gamma (ZAG) approach. For proportional data, the book shows the use of the binomial and the beta distributions.

The third layer of complexity is pseudo-replication. Researchers frequently have multiple observations from the same site, animal, person, etc. This brings you within the world of linear mixed-effects models and generalised linear mixed models (GLMMs). This is the topic of volume 2.

The fourth layer of complexity is that some covariates may have a non-linear effect, which may require generalised additive models (GAMs). If your data sets require zero-inflated GAM or zero-inflated generalized additive mixed models (GAMMs), then Volume 4 of this series will help you analyse your data. If on top of this, you also have spatial, temporal, or spatial-temporal dependency, then there is no escape from R-INLA. Note that with spatial dependency, the assumption is that you have 50+ spatial locations. And temporal dependency becomes relevant if you have 15+ measurements over time. Zero-inflated spatial and spatial-temporal models are discussed in Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA, Volume 2 GAM and Zero-Inflated Models.