An application of Poisson Gaussian regresssion

In this study, Poisson, negative binomial and Poisson inverse Gaussian regression models were used to model the effect of month, temperature and humidity variables on mite counts. It was concluded that Poisson regression should not be used due to the high over-spread in the dependent variable. This is reflected in both Poisson model fit statistics and parameter estimates and significance levels. However, the performance of negative binomial and Poisson inverse Gaussian regressions were similar. The Poisson inverse Gaussian regression performed better than the negative binomial regression in terms of fit measures. The parameter estimation values and significance levels of both regression models were parallel. When all three regression models used in the study are evaluated together, it is seen how much change the over-spread causes on the estimates. The difference between the two models is the distributions they use. Poisson inverse Gaussian regression is similar to negative binomial regression, but there is a difference between these two models. While negative binomial regression is a mixture of Poisson and gamma distributions, Poisson inverse Gaussian regression is a mixture of Poisson and inverse Gaussian distributions. However, the performances of these two regression models can be compared with different degrees of deletion of observations in the dependent variable.