Extended negative binomial hurdle models

Abstract

Poisson models are widely used for statistical inference on count data. However, zero-inflation or zero-deflation with either overdispersion or underdispersion could occur. Currently, there is no available model for count data, that allows excessive occurrence of zeros along with underdispersion in non-zero counts, even though there have been reported necessity of such models. Furthermore, given an excessive zero rate, we need a model that allows a larger degree of overdispersion than existing models. In this paper, we use a random-effect model to produce a general statistical model for accommodating such phenomenon occurring in real data analyses.

Keywords

Excessive zeros hierarchical generalized linear model Poisson hurdle model underdispersion zero-inflated Poisson model

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References

Johnson

Kotz

Kemp

. Univariate discrete distributions, 2nd ed. New York, NY: Wiley, 1992.

Morgan

. Some stochastic models to describe the fertilization of an egg. Appl Stat 1975; 24: 137–138.

Morgan

BJT

. Modelling polyspermy. Biometrics 1982; 38: 885–898.

Daley

Maindonald

. A unified view of models describing the avoidance of superparasitism. IMA J Math App Biol Med 1989; 6: 161–178.

Griffiths

. Avoidance-modified generalised distributions and their application to studies of superparasitism. Biometrics 1977; 33: 103–112.

Singh

. A note on inflated Poisson distribution. J Ind Statist Assoc 1963; 1: 140–144.

Lambert

. Zero-inflated Poisson regression with an application to defects in manufacturing. Technometrics 1992; 34: 1–14.

Cragg

. Some statistical models for limited dependent variables with application to the demand for durable goods. Econometrica 1971; 39: 829–844.

Mullahy

. Specification and testing of some modified count data models. J Econom 1986; 33: 341–365.

10.

Lee

Alam

Noh

et al.

Spatial model with excessive zero counts for analysis of the changes in reindeer distribution. Ecol Evol 2016; 6: 7047–7056.

11.

Lee

Nelder

. Hierarchical generalized linear models. J R Statist Soc B 1996; 58: 619–678.

12.

Chernyavskiy

Little

Rosenberg

. Correlated Poisson models for age-period-cohort analysis. Stat Med 2018; 37: 405–424.

13.

Moloas

Lesaffre

. Hurdle models for multilevel zero-inflated data via h-likelihood. Stat Med 2010; 29: 3294–3310.

14.

Tin A. Modeling zero-inflated count data with underdispersion and overdispersion. SAS Global Forum, Statistics and Data Analysis 2008

15.

Lee Y, Nelder JA and Pawitan Y. Generalized linear models with random effects, unified analysis via H-likelihood. 2nd ed. London: Chapman & Hall/CRC, 2017

16.

Deb

Trivedi

. Demand for medical care by the elderly: a finite mixture approach. J Appl Econom 1997; 12: 313–326.

17.

Zorn

CJW

. Evaluating zero-inflated and hurdle Poisson specifications. Midw Polit Sci Assoc 1996, pp. 1–16.

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