Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

This study developed a Bivariate Zero-Inflated Poisson Inverse Gaussian Regression (BZIPIGR) model to presents the form of BZIPIGR parameter estimation and modeling of the number of HIV and AIDS cases in each sub-district in Trenggalek and Ponorogo regencies to determine the factors that have a significant effect. This model can be used on data that have overdispersion cases caused by extra zeros in the response variables. The parameter estimation of the BZIPIGR model uses the Maximum Likelihood Estimation (MLE). The first derivative of the BZIPIGR model has obtained not closed form, therefor it has continued with the Berndt Hall Hall Hausman (BHHH) iteration to obtain the maximum likelihood estimators, while the hypothesis testing of the BZIPIGR model is derived using Maximum Likelihood Ratio Test (MLRT) approach. Based on the AICc value obtained, the BZIPIGR model is a feasible model to be applied to data on the number of HIV and AIDS cases in Trenggalek and Ponorogo Districts, East Java Province. The variable that had a significant effect on the increase in the number of HIV and AIDS cases was the percentage of the population with low education (SMA). The variables that had a significant effect on reducing the number of HIV and AIDS cases were the percentage of the population aged 25-29 years, the percentage of reproductive-age couples using condoms, the percentage of health educations activities about HIV and AIDS, and the percentage of community health insurance (Jamkesmas).