[R] Goodness-of-fit of GLM for Gamma Distribution

Fredrik Odegaard fodegaar at gmail.com
Thu Oct 11 17:26:56 CEST 2007

Hi All,
could someone please shed some light on the proper goodness-of-fit
analysis for the GLM output based on Gamma distributions with the

My objective is to test the goodness-of-fit for the final model (and
not the comparison of nested models).

In particular, should the 'Residual Deviance' be compared with the
Chi-Square distribution, or should the 'Scaled Residual Deviance',
i.e. the Residual Deviance divided by the dispersion estimator, be
compared with the Chi-Square distribution. Or alternatively, using
(7.10) in Venables&Ripley (p.187 MASS 4th) and compare the scaled
residual deviance with the appropriate F distribution. Below I have
included a sample output from one model. And my concern is if the
residual deviance should be divided by the dispersion parameter.

Many thanks for any insight or comments.

Fredrik Odegaard

Null Deviance: 357.12 on 394 d.f.
Residual Deviance: 333.51 on 391 d.f.
Dispersion parameter: .5551945

Pearson X^2: 217.0827

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