4 Goodness test
The deviance information criterion is the statistic used to assess the goodness of fit of the Poisson regression. It is calculated as the difference in log likelihoods between the two models then multiplied by -2. For large samples the distribution of the deviance is approximately a Chi-squared with n-p degrees of freedom, where n is the number of observations and p the number of parameters [1]. A significant p value indicates that the deviance is greater than what would be expected under a null hypothesis of model equivalence; hence, the more complex model with an additional parameter or parameters is considered a significant improvement over the nested model [20].