### 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 language | English |
---|---|

Pages (from-to) | 515-529 |

Number of pages | 15 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 43 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Feb 2014 |

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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.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 43, no. 3, pp. 515-529. https://doi.org/10.1080/03610926.2012.665553

}

TY - JOUR

T1 - Functional form for the zero-inflated generalized poisson regression model

AU - Zamani, Hossein

AU - Ismail, Noriszura

PY - 2014/2/1

Y1 - 2014/2/1

N2 - 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.

AB - 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.

KW - Functional form

KW - Overdispersion

KW - Zero-inflated generalized Poisson

KW - Zero-inflated Poisson

KW - Zero-inflation

UR - http://www.scopus.com/inward/record.url?scp=84892689252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892689252&partnerID=8YFLogxK

U2 - 10.1080/03610926.2012.665553

DO - 10.1080/03610926.2012.665553

M3 - Article

AN - SCOPUS:84892689252

VL - 43

SP - 515

EP - 529

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 3

ER -