### A Comparison of Quasi-Poisson and Zero Inflated Negative Binomial Regression Models for Over-dispersion Count Data

#### Abstract

In this research study aimed to compare the appropriation of regression models between Quasi-Poisson (QP) and Zero inflated negative binomial (ZINB) which dependent variable was count data and the variance was greater than the mean. The dependent variable for the real data was the number of injured in each accident which there are three cases: small (=17), medium (=32) and large (=56). The probabilities of zero event () were 0.25 for the small sample size and 0.50 for the medium and large sample sizes. In the real data set, there are three independent variables. For the simulation data, the dependent variable had Zero inflated negative binomial distribution. The dispersion parameter of the distribution () were 1.25, 1.50 and 1.75, the probability of zero events () were 0.25 and 0.50 and the mean () were 1.4, 2 and 3. For the simulation data set, Three independent variables were determined with bernoulli distribution and the probability of success events () were 0.3, 0.5 and 0.8. The sample size of the simulation data () were small (=15, 20), medium (=30, 35) and large (=45, 50). The criteria of model appropriation were root mean square error (RMSE) and absolute average error (AAE). The smaller values of RMSE or AAE indicate the better model. For the results based on RMSE and AAE, it is found that the Quasi-Poisson regression model was more appropriate than Zero inflated negative binomial regression model at almost case of study for both the real and simulation data.

**Keywords : *** *count data, over-dispersion, Quasi-Poisson Regression model, Zero inflated negative binomial

regression model

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