Zero Inflated Bivariate Ordered Probit on Poverty Levels in Eastern Indonesia - Andriano; Purhadi; Ismaini Zain (Department of Statistics ITS, 2026)
This study examines the development of a bivariate ordinal probit regression model with zero-inflated effects. The bivariate ordinal probit regression method that can overcome zero-inflated effects is the Zero Inflated Bivariate Ordered Probit (ZIBOPR) method. ZIBOPR is a statistical method for examining the relationship between predictor variables and two correlated response variables that have levels and zero-inflated effects. A theoretical study was conducted to obtain parameter estimates for the ZIBOPR model using the Maximum Likelihood Estimator (MLE) method. The estimation equation obtained from MLE produces a non-closed form equation, so it is continued with the Bern, Hall, Hall, and Hausman (BHHH) numerical iteration method. The resulting parameters are then tested simultaneously with the Likelihood Ratio Test (LRT) and individually using the Wald test. The ZIBOPR model was applied to the case of the percentage of poor people and the poverty depth index in 176 districts/cities in Eastern Indonesia in 2023 using five predictor variables, namely life expectancy, per capita expenditure, average length of schooling, Labor Force Participation Rate (LFPR), and Infant Mortality Rate (IMR). The results showed that the ZIBOPR model parameters could be estimated using MLE and followed by BHHH numerical iteration. The resulting parameters could then be tested simultaneously using LRT and individually using the Wald test. Subsequently, ZIBOPR modeling with poverty rate levels and poverty depth index levels showed that the five parameters in the predictor variables had a significant effect on poverty rate levels and poverty depth index levels. The results of the best model selection analysis using the vuong test show that the ZIBOPR model better models the percentage of poor population and the poverty depth index than the bivariate ordinal probit regression model.