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In a GLM, how should I interpret the difference between using

  1. sum of the model's Pearson residuals
  2. 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"?

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