Modelling Data That Exhibit an Excess Number of Zeros: Zero-Inflated Models and Generic Mixture Models

Abstract

In biomedical research, data generated as a consequence of the count process can often possess an ‘excess’ of zeros (e.g. geographical incidence rates, hospital death rates). Whilst there are strategies for analysing such data, some can be biased where the underlying data generation process is not carefully considered. This can be exacerbated where the data are also multilevel, since hierarchical extensions to zero-inflated model strategies do not always satisfy underlying model assumptions. We therefore review zero-inflated modelling strategies for single-level data and show why standard Poisson and binomial zero-inflated models (i.e. where one latent class has a central location of zero) require class membership to be predicted by covariates in the standard regression part of the model. We also introduce generic mixture models and reveal limitations in their interpretation in a number of circumstances. With nested or hierarchical count data with an excess of zeros, upper-level distributional assumptions may not be upheld for standard multilevel models, thereby requiring alternative strategies; in Chap. 7 we introduce and illustrate the semi-parametric multilevel model as a solution to this problem.