Simulation Study of Bayesian Hurdle Poisson Regression on the Number of Deaths from Chronic Filariasis in Indonesia

Abstract

One regression model to explain the relationship between predictor and response variable in the form of count is Poisson regression. In the case of certain Poisson with the presence of many zero values, causing overdispersion can be overcome with the Poisson Hurdle model. There is a good method for estimating the parameters on small sample sizes for all distributions, namely the Bayesian method. The response variable of the original data does not follow Poisson distribution, so parameter will be estimated by Bayesian method. The performance of the Bayesian Hurdle Poisson regression can be seen from simulation data on various sample sizes and overdispersion levels generated based on the parameters of original data showing that the Bayesian Hurdle Poisson regression model proposed in this study is suitable for large sample sizes or with varying levels of overdispersion due n ≥ 30 or n → ∞ because normal distribution is used as prior. Even though the response variable of the simulation data is generated with a Poisson distribution, it still does not follow a Poisson distribution because it’s in accordance with the original data. The parameter estimated based on the simulation data is similar to the parameter estimated on the original data (both the estimator of the MLE Hurdle Poisson regression parameter and the parameter estimator of the Bayesian Hurdle Poisson regression). This indicates that the simulation scenario is appropriate.