Simulation on the Zero Inflated Negative Binomial (ZINB) to Model Overdispersed, Poisson Distributed Data

Abstract Poisson regression analysis shows the relationship between predictor variables and response variables that follow the Poisson distribution which has equal dispersion and average values (λ), a situation called equidispersion. However, the variance can also be greater than the average value, called overdispersion. This can be caused by excess opportunities for the emergence of zero values in the response variable or zero excess. The parameter of the overdispersed data analysis can be underestimated so that the results become biased. This bias issue can be, hopefully, overcome by the Zero Inflated Negative Binomial (ZINB) regression analysis. In the 2016 Maternal Mortality Rate data in Bojonegoro District, overdipersion was overcome by ZINB regression even though there was no significant predictor variable found affecting the response variable. ZINB regression analysis can also be applied to generated data (simulation). We had the data with average λ = (0.2, 0.4, 0.6, 0.8, 1.0, 5.0) proportion of zeros p = (0.4, 0.6, 0.8), and the number of observationsn = (200,500, 800), with each setting was repeated 100 times. From the simulation study it was found that all overdispersion events were always accompanied by zero excess events but not vice versa. The greater the value of λ then the greater the dispersion coefficient. The ZINB regression is proven to be able to overcome overdispersion in various conditions of different values of λ, p, n which can be seen from the value τ (dispersion coefficient) after ZINB regression is less than 1 in all conditions.