### Abstract

Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.

Original language | English |
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Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | Journal of Statistical Computation and Simulation |

DOIs | |

Publication status | Accepted/In press - 29 Jul 2016 |

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### Keywords

- Bivariate counts
- healthcare
- negative binomial
- zero-inflation

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

**Bivariate zero-inflated negative binomial regression model with applications.** / Faroughi, Pouya; Ismail, Noriszura.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Bivariate zero-inflated negative binomial regression model with applications

AU - Faroughi, Pouya

AU - Ismail, Noriszura

PY - 2016/7/29

Y1 - 2016/7/29

N2 - Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.

AB - Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.

KW - Bivariate counts

KW - healthcare

KW - negative binomial

KW - zero-inflation

UR - http://www.scopus.com/inward/record.url?scp=84980049318&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980049318&partnerID=8YFLogxK

U2 - 10.1080/00949655.2016.1213843

DO - 10.1080/00949655.2016.1213843

M3 - Article

SP - 1

EP - 21

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

ER -