# For an adequate fit of GLM models [duplicate]

I am trying to understand how to test for the goodness of fit in GLM regression. I am using an example from the book Davison and Hinkley (1997). In R, they fit the following model:

data(cane) # this dataset is available by default
cane.glm <- glm(y ~ block+var,family=binomial,data=cane)
summary(cane.glm)


Then they write that "for an adequate fit, the deviance would roughly be distributed according to a $\chi^2_{132}$ (where $132$ is the residual degrees of freedom of the regression); in fact, it is 1142.8; This indicates overdispersion relative to the model." They, however, miss to provide more details on how to proceed.

I think I need to compute the deviance deviance(cane.glm) and use pachisq function to test whether the observed value is far away from the theoretical distribution. I don't understand, however, the exact testing procedure. Any example in R would be much appreciated.

In addition, this reference (p.8) suggest that this type of "goodness of fit" test "does not actually work very well." Why not? What else should I use?

• Why would you need to test anything? 1142.8 is plainly very deep into the tail of a chi-square with 132 d.f. (which has mean 132 and s.d. $\sqrt{2\times 132}\approx 16.25)$... what more would a test tell you? But in any case the question isn't "are these data drawn from this specific Poisson GLM?" (they aren't and with enough data a test would always tell you so) but whether the model is a suitable description, and for that, knowing that the deviance is nearly 9 times as big as you'd expect it to be (with consequent impact on inference) is the thing that leads us to look for what's wrong. Jul 15 '17 at 23:07
• It's a pity the author of your linked notes doesn't offer a full reference for Hosmer et al 1997 which would probably explain the "doesn't work well" claim. I wonder if the intent was "A comparison of goodness of fit tests for the logistic regression model", Statistics in Medicine, 16, 965-980 ... If that's the reference, its relevance to Poisson regression is not immediately clear, however. Jul 15 '17 at 23:47
• I don't see a cane dataset that is loaded automatically. Are you referring to ?cane in the boot package? There is no y variable in that dataset. How did you construct it, y = with(cane, cbind(r, n-r))? Aug 5 '17 at 21:30