Parameters Estimation and Model Hypotesis Testing On Bivariate Zero-Inflated Negative Binomial Regression
Rahmania Azwarini (a*), Purhadi (a**), Achmad Choiruddin (a)

a) Department of Statistics, Faculty of Science and Data
Analytics, Institut Teknologi Sepuluh Nopember, Arief Rahman Hakim Street, Surabaya 60111, Indonesia.
*rahmaniaazwarini[at]gmail.com
**purhadi[at]statistika.its.ac.id

Abstract

Poisson regression is a regression model that commonly used to model count data. Unfortunately, the Poisson regression modelling on the count data can be failed, which can be caused by overdispersion. Overdispersion is a condition when the variance value is greater than the mean value in the data. Overdispersion can be caused by two aspects, namely overdispersion due to unobserved sources of diversity in the data and overdispersion due to excess zeros in the data. Therefore, this research developed a model that can handle issues that cause overdispersion especially at bivariate count data, namely Bivariate Zero-Inflated Negative Binomial (BZINBR). BZINBR model has the advantages that it does not require the same variance values as the average value, and there is dispersion parameter to describe the variation of the data. BZINBR model can be applied to count data that consist of two response variables. This research focuses on the development of BZINBR type II to deal with overdispersion issues, where the BZINBR type II model has response variables that consists of several combinations pairs of Y values. This study also proposes an efficient algorithm for parameter estimation using the Maximum Likelihood Estimation (MLE) method followed by Berndt-Hall-Hall- Hausman (BHHH) iterations and testing hypotheses using the Maximum Likelihood Ratio Test (MLRT) method. The results of this study are expected to be source of new knowledge for readers in statistical science, particularly related to the BZINBR model.

Keywords: Bivariate Zero-Inflated Negative Binomial- BHHH- MLE- MLRT- Overdispersion

Topic: Mathematics and Statistics