Bivariate zero-inflated negative binomial regression model with applications

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.

KEYWORDS:

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgements

The authors are also grateful to the anonymous referees and the Associate Editor for their valuable comments and suggestions.

Additional information

Funding

The authors gratefully acknowledge the financial support received in the form of research university grants (GUP-2015-002 and FRGS/1/2015/SG04/UKM/02/2) from the Universiti Kebangsaan Malaysia (UKM) and the Ministry of Higher Education (MOHE), Malaysia.