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 probabilities deviate from the observed probabilities in a way that the multinomial distribution does not predict. The test is not useful when the number of distinct values is approximately equal to the number of observations, but the test is useful when you have multiple observations at the same values of the predictors. If the p-value for the goodness-of-fit test is lower than your chosen significance level, the predicted probabilities deviate from the observed probabilities in a way that the multinomial distribution does not predict. This list provides common reasons for the deviation:
- 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.