In a GLM, how should I interpret the difference between using
- sum of the model's Pearson residuals
- model's Deviance
to assess the fit of my model? Is the former more "flexible" since I can estimate a dispersion parameter? I feel like the Deviance provide a more parametric assessment since it takes the form of the ML equations we're using to fit the model whereas the Pearson residuals feel one step removed. Is this right / which is more "parametric"?