Zero Inflated Models and Generalized Linear Mixed Models with R

Chapter 1 provides a basic introduction to Bayesian statistics and Markov Chain Monte Carlo (MCMC), as we will need this for most analyses. If you are familiar with these techniques we suggest quickly skimming through it. In Chapter 2 we analyse nested zero inflated data of sibling negotiation of barn owl chicks. We explain application of a Poisson GLMM for 1-way nested data and discuss the observation-level random intercept to allow for overdispersion. We show that the data are zero inflated and introduce zero inflated GLMM. We recommend reading this chapter in detail, as we will refer often to it. Data of sandeel otolith presence in seal scat is analysed in Chapter 3. We present a flowchart of steps in selecting the appropriate technique: Poisson GLM, negative binomial GLM, Poisson or negative binomial GAM, or GLMs with zero inflated distribution. Chapter 4 is relevant for readers interested in the analysis of (zero inflated) 2-way nested data. The chapter takes us to marmot colonies: multiple colonies with multiple animals sampled repeatedly over time. Chapters 5 - 7 address GLMs with spatial correlation. Chapter 5 presents an analysis of Common Murre density data and introduces hurdle models using GAM. Random effects are used to model spatial correlation. In Chapter 6 we analyse zero inflated skate abundance recorded at approximately 250 sites along the coastal and continental shelf waters of Argentina. Chapter 7 also involves spatial correlation (parrotfish abundance) with data collected around islands, which increases the complexity of the analysis. GLMs with residual conditional auto-regressive correlation structures are used. In Chapter 8 we apply zero inflated models to click beetle data. Chapter 9 is relevant for readers interested in GAM, zero inflation, and temporal auto-correlation. We analyse a time series of zero inflated whale strandings. In Chapter 10 we demonstrate that an excessive number of zeros does not necessarily mean zero inflation. We also discuss whether the application of mixture models requires that the data include false zeros and whether the algorithm can indicate which zeros are false.