Comparing Poisson-Inverse Gaussian Model and Negative Binomial Model on case study: horseshoe crabs data

Poisson Regression analysis is commonly used for dependent variable that has non-negative value, called count data. Poisson Regression has an assumption that mean of dependent variable equal to its variance. On over dispersion case where the variance is greater than mean, poisson regression is inconvenient to used because it may underestimate the standard error of regression parameters and consequently giving misleading inference. Poisson-Inverse Gaussian and Negative Binomial regression model can be used on over dispersion data. This paper will discuss about Poisson-Inverse Gaussian regression model, Negative Binomial regression model and comparing them in terms of Goodness-of-fit (GOF) statistics on case study of horseshoe crabs data. According to the result, pseudo R-squared value of P-IG regression model is greater than the Negative Binomial regression model. It shows that P-IG regression model is better than Negative Binomial regression model.