When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximate?

I’ve often seen the advice for checking whether or not a Poisson model fit is over-dispersed involving dividing the residual deviance by the degrees of freedom. The resulting ratio should be “approximately 1”.

The question is what range are we talking about for “approximate” – what is a ratio that should set off alarms to go consider alternative model forms?

Answer

10 is large… 1.01 is not. Since the variance of a χ2k is 2k (see Wikipedia), the standard deviation of a χ2k is 2k, and that of χ2k/k is 2/k. That’s your measuring stick: for χ2100, 1.01 is not large, but 2 is large (7 s.d.s away). For χ210,000, 1.01 is OK, but 1.1 is not (7 s.d.s away).

Attribution
Source : Link , Question Author : Fomite , Answer Author : StasK

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