I'm a little confused about the different common tests for GLMs.
There is the null deviance, which is similar to a likelihood ratio for the difference between the saturated model and the model with only an intercept.
There is the residual deviance, which is similar to a likelihood ratio for the difference between the saturated model and the current fitted model.
It seems to me that you can use the difference in residual and null deviance, which should follow a Chi-square distribution, to give something analogous to the F-test in regression, is this correct?
You can test the residual deviance itself, as it allows you to determine goodness of fit?
I'm assuming there is no test involving the null deviance alone
Unrelated to deviances, you can do likelihood ratio tests comparing for example a model with all parameters and a model lacking one of them?
R just outputs the null deviance and the residual deviance along with their degrees of freedom, so I assume the point is that you can use them to do the tests mentioned above.
If someone can elaborate (on a basic level) I would really appreciate it, because I'm really getting confused as to what the GLM tests make use of in terms of deviance etc.. And if I missed any tests please let me know as well.