# Chi Square vs F Tests for GLM Model Comparisons

I've been creating some models in R using glm() and rxGlm(). I'm experienced in building GLMs but my memory of some of the underlying theory is a little rusty.

I'm interested in comparing model fits for nested models using chi-square tests, F tests, etc.

I'm able to compare nested glm model objects using

anova (model1, model2, test = "Chisq")


etc. From reading around the subject a little, it seems that chi-square is only valid for certain GLMs - those where the scale parameter is fixed (Poisson & binomial), whereas the F test should be used where the scale parameter is estimated (eg normal, gamma). Is this correct?

I have a particular interest in creating GLMs using the Tweedie family of distributions. Is this a case where F would be preferable to chi-square?

Basically, yes. $$F$$ is used when the dispersion parameter is estimated rather than assumed to be fixed to some known value. $$F$$ is also often used for quasi-likelihood models where a somewhat ad hoc overdispersion parameter is estimated (see e.g. Venables and Ripley Modern Applied Statistics with S).