A Study of ZIP and ZINB Regression Modeling for Count Data with Excess Zeros

Abstract

Count data with excess number of zeros can cause overdispersion problems. Overdispersion is the presence of greater variability in a data set than would be expected. Overdispersion due to zero-inflated data can be handled either by Zero-inflated Poisson (ZIP) regression or Zero-inflated Negative Binomial (ZINB) regression. In this paper, the performances of different models have been compared based on their MSE, RMSE, bias, and AIC using simulation. The simulated data were generated using ZIP and ZINB distributions. The data were generated using a combination of observation size (n), mean (µ), and the proportion of zeros observation (ω) were imposed to facilitate comparison. To ensure the present of overdispersion, the score test has been applied to the generated data. As expected, the results showed that ZIP and ZINB regression performed better when compared to the Poisson regression. Moreover, in general the simulation results showed that ZINB regression showed better performance than ZIP and Poisson regressions. In this paper, ZINB regression was applied to analyze maternal mortality rate in East Java. The results showed that maternal mortality was significantly affected by the percentage of pregnant woman visiting the clinics for the first time as well as by the percentage of pregnant woman visiting clinics for the fourth time.