Functional form for the zero-inflated generalized poisson regression model

Hossein Zamani, Noriszura Ismail

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The generalized Poisson (GP) regression is an increasingly popular approach for modeling overdispersed as well as underdispersed count data. Several parameterizations have been performed for the GP regression, and the two well known models, the GP-1 and the GP-2, have been applied. The GP-P regression, which has been recently proposed, has the advantage of nesting the GP-1 and the GP-2 parametrically, besides allowing the statistical tests of the GP-1 and the GP-2 against a more general alternative. In several cases, count data often have excessive number of zero outcomes than are expected in the Poisson. This zero-inflation phenomenon is a specific cause of overdispersion, and the zero-inflated Poisson (ZIP) regression model has been proposed. However, if the data continue to suggest additional overdispersion, the zero-inflated negative binomial (ZINB-1 and ZINB-2) and the zero-inflated generalized Poisson (ZIGP-1 and ZIGP-2) regression models have been considered as alternatives. This article proposes a functional form of the ZIGP which mixes a distribution degenerate at zero with a GP-P distribution. The suggested model has the advantage of nesting the ZIP and the two well known ZIGP (ZIGP-1 and ZIGP-2) regression models, besides allowing the statistical tests of the ZIGP-1 and the ZIGP-2 against a more general alternative. The ZIP and the functional form of the ZIGP regression models are fitted, compared and tested on two sets of count data; the Malaysian insurance claim data and the German healthcare data.

Original languageEnglish
Pages (from-to)515-529
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Volume43
Issue number3
DOIs
Publication statusPublished - 1 Feb 2014

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Poisson Regression
Poisson Model
Regression Model
Siméon Denis Poisson
Zero
Count Data
Overdispersion
Statistical test
Form
Alternatives
Zero-inflation
Negative Binomial
Insurance
Parameterization
Healthcare
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Keywords

  • Functional form
  • Overdispersion
  • Zero-inflated generalized Poisson
  • Zero-inflated Poisson
  • Zero-inflation

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Functional form for the zero-inflated generalized poisson regression model. / Zamani, Hossein; Ismail, Noriszura.

In: Communications in Statistics - Theory and Methods, Vol. 43, No. 3, 01.02.2014, p. 515-529.

Research output: Contribution to journalArticle

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