The deviance goodness-of-fit test assesses the discrepancy between the current model and the full model.
Use the goodness-of-fit tests to determine whether the predicted numbers of events deviate from the observed numbers of events in a way that the Poisson distribution does not predict. If the p-value for the goodness-of-fit test is lower than your chosen significance level, you can reject the null hypothesis that the Poisson distribution provides a good fit. This list provides common reasons for deviations:
- Incorrect link function
- Omitted higher-order term for variables in the model
- Omitted predictor that is not in the model
If the deviation is statistically significant, you can try a different link function or change the terms in the model.