Haslett, John and Parnell, Andrew and Hinde, John and de Andrade Moral, Rafael (2021) Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches. International Statistical Revie. ISSN 0306-7734

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Abstract

We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: over-dispersion (OD) models and zero-inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as implicit and explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by-product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the apparent excess of zeros in the counts. Typically, the modelling of the excess zeros per se is a secondary objective, and there are choices to be made between, and within, the OD and ZI approaches. The contribution of this paper is primarily conceptual. We contrast, descriptively, the impact on zeros of the two approaches. We further offer a novel descriptive characterisation of alternative ZI models, including the classic hurdle and mixture models, by providing a unifying theoretical framework for their comparison. This in turn leads to a novel and technically simpler ZI model. We develop the underlying theory for univariate counts and touch on its implication for multivariate count data.

Item Type:	Article
Additional Information:	© 2021 The Authors. International Statistical Review published by John Wiley & Sons Ltd on behalf of International Statistical Institute. This is an open access article under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Cite as: Haslett, J., Parnell, A. C., Hinde, J., and de Andrade Moral, R. (2021) Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches. International Statistical Review, https://doi.org/10.1111/insr.12479.
Keywords:	hurdle; over-dispersion; zero-altered; zero-deflation; zero-inflation;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	15514
Identification Number:	https://doi.org/10.1111/insr.12479
Depositing User:	Rafael de Andrade Moral
Date Deposited:	15 Feb 2022 16:51
Journal or Publication Title:	International Statistical Revie
Publisher:	Wiley
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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