Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression

Kimberly F. Sellers; Derek S. Young

doi:10.1080/00949655.2019.1590580

Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression

Kimberly F. Sellers, Derek S. Young

Dr. Bing Zhang Department of Statistics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

While excess zeros are often thought to cause data over-dispersion (i.e. when the variance exceeds the mean), this implication is not absolute. One should instead consider a flexible class of distributions that can address data dispersion along with excess zeros. This work develops a zero-inflated sum-of-Conway-Maxwell-Poissons (ZISCMP) regression as a flexible analysis tool to model count data that express significant data dispersion and contain excess zeros. This class of models contains several special case zero-inflated regressions, including zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-inflated binomial (ZIB), and the zero-inflated Conway-Maxwell-Poisson (ZICMP). Through simulated and real data examples, we demonstrate class flexibility and usefulness. We further utilize it to analyze shark species data from Australia's Great Barrier Reef to assess the environmental impact of human action on the number of various species of sharks.

Original language	English
Pages (from-to)	1649-1673
Number of pages	25
Journal	Journal of Statistical Computation and Simulation
Volume	89
Issue number	9
DOIs	https://doi.org/10.1080/00949655.2019.1590580
State	Published - Jun 13 2019

Bibliographical note

Funding Information:
Support for Kimberly Sellers was provided in part by the American Statistical Association (ASA)/ National Science Foundation (NSF)/ Census Research Program, U. S. Census Bureau Contract #YA1323-14-SE-0122. This paper is released to inform interested parties of research and to encourage discussion. The views expressed are those of the authors and not necessarily those of the U.S. Census Bureau.

Funding Information:
Support for Kimberly Sellers was provided in part by the American Statistical Association (ASA)/ National Science Foundation (NSF)/ Census Research Program, U. S. Census Bureau Contract #YA1323-14-SE-0122. This paper is released to inform interested parties of research and to encourage discussion. The views expressed are those of the authors and not necessarily those of the U.S. Census Bureau. The authors thank the anonymous reviewers for their insightful comments that helped improve the manuscript. The authors also thank Sophie Lockwood (Georgetown University) for her assistance.

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

Count data modelling
discrete data
over-dispersion
under-dispersion
zero-inflated Poisson
zero-inflated negative binomial

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/00949655.2019.1590580

Cite this

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title = "Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression",

abstract = "While excess zeros are often thought to cause data over-dispersion (i.e. when the variance exceeds the mean), this implication is not absolute. One should instead consider a flexible class of distributions that can address data dispersion along with excess zeros. This work develops a zero-inflated sum-of-Conway-Maxwell-Poissons (ZISCMP) regression as a flexible analysis tool to model count data that express significant data dispersion and contain excess zeros. This class of models contains several special case zero-inflated regressions, including zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-inflated binomial (ZIB), and the zero-inflated Conway-Maxwell-Poisson (ZICMP). Through simulated and real data examples, we demonstrate class flexibility and usefulness. We further utilize it to analyze shark species data from Australia's Great Barrier Reef to assess the environmental impact of human action on the number of various species of sharks.",

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Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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