Bivariate Poisson Inverse Gamma INAR(1) Regression Model: Healthcare Service Visits by Health Insurance Members Case Study

The integer-valued Autoregressive (INAR) model is a statistical approach for modeling positive integer time series data. There are two components in the INAR model: the correlation structure, which utilizes a binomial thinning operator, and the marginal distribution, which is mixed Poisson. Accommodating strict assumptions in Poisson, Inverse gamma is chosen as the associated mixing distribution because of its good performance in accommodating overdispersion data with heavy tails. The Bivariate Poisson Inverse Gamma INAR (1), BPIGA-INAR(1), is proposed to model and analyze a positive integer time series data set from Badan Penyelenggara Jaminan Sosial (BPJS) in Indonesia. The data set provides information about the total number of healthcare service visits by health insurance members diagnosed with diabetes and heart disease from 2015 to 2020. The parameter estimation process is conducted using Maximum Likelihood Estimation (MLE) and Genetic Algorithms (GA), while the Maximum Likelihood Ratio Test (MLRT) is used for hypothesis testing. BPIGA-INAR(1) model was established as a suitable model for the data set, with age and gender have significant impacts on the number of healthcare service visits by each health insurance member diagnosed with diabetes disease and the inclusion of an 'unemployed' category in the Membership segment for heart disease.