Check out my chapter in Gordon Fox, Simoneta Negrete-Yankelevich, and Vinicio Sosa’s new ecological statistics book: https://global.oup.com/academic/product/ecological-statistics-9780199672554?cc=au&lang=en&
Ecological data rarely meet the assumptions of the standard probably distributions that are used in most statistical models – in particular, our data are often overdispersed (that is, the variance of our data is higher than can be accommodated by standard distributions). One particularly common source of overdispersion is zero-inflation where our data have too many zeros. See a previous paper of ours on zero-inflation here. But how do we deal with these types of non-standard data issues!
In this chapter I address this by focussing on how we can use mixture models (which are combinations of two or more probability distributions) to deal with the general issue of overdispersion. I demonstrate that, not only can mixture models help to account for overdispersion, but they are also very useful for identifying the ecological or observation processes that lead to the overdispersion. Thus the approach is a powerful method for improved ecological inference. I illsutrate this using case studies on modelling koala poo decay and lemur abundance and provide R code to fit the models.
Given the prevalence of overdispersion in ecological data, mixture models should form a key part of the ecologist’s statistical toolbox. This chapter aims to give guidance on how to use and apply these types of models.