Bivariate negative binomial regression model with excess zeros and right censoring: an application to Indonesian data

We propose a bivariate hurdle negative binomial (BHNB) regression model with right censoring to model correlated bivariate count data with excess zeros and few extreme observations. The parameters of the BHNB regression model are obtained using maximum likelihood with conjugate gradient optimization. The proposed model is applied to actual survey data where the bivariate outcome is number of days missed from primary activities and number of days spent in bed due to illness during the 4-week period preceding the inquiry date. We compared the right censored BHNB model to the right censored bivariate negative binomial (BNB) model. A simulation study is conducted to discuss some properties of the BHNB model. Our proposed model demonstrated superior performance in goodness-of-fit of estimated frequencies.