Complete the following steps to interpret a Poisson regression model. Key output includes the p-value, coefficients, model summary statistics, and the residual plots.

To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.

- P-value ≤ α: The association is statistically significant
- If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response variable and the term.
- P-value > α: The association is not statistically significant
- If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. You may want to refit the model without the term.

If a model term is statistically significant, the interpretation depends on the type of term. The interpretations are as follows:

- If a continuous predictor is significant, you can conclude that the coefficient for the predictor is different from zero.
- If a categorical predictor is significant, you can conclude that not all of the levels have the same mean number of events.
- If an interaction term is significant, you can conclude that the relationship between the predictor and the number of events depends on the other predictors in the term.
- If a polynomial term is significant, you can conclude that the relationship between a predictor and the number of events depends on the magnitude of the predictor.

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
- Overdispersion

If the deviation is statistically significant, you can try a different link function or change the terms in the model.

Use AIC, AICc, and BIC to compare different models. For each statistic, smaller values are desirable. However, the model with the smallest value for a set of predictors does not necessarily fit the data well. Also use goodness-of-fit tests and residual plots to assess how well a model fits the data.