In this book, p.334 (348 for pdf) it says you can model a binomial regression in a few ways:
response as an observed proportion, with weights. e.g.
fit = glm(s/n ~ factor(group), weights=n, family="binomial")
response is given as 2 columns array:
fit = glm(cbind(Fissures, Turbines-Fissures) ~ Hours, family="binomial")
response given as a factor (i.e. each row is a single Bernoulli trial):
fit = glm(y ~ factor(group), family="binomial")
I ran options 1 and 3 on my dataset, and I get the exact same coefficients and p.values for them, BUT the Deviance and DF are different - for 1 I get that the residual deviance is too high, but for 3 it's actually very low.
Further in the chapter it is said that there are no Goodness-of-Fit for Binary Responses (i.e. for 3 I should ignore the residual-deviance), because:
"In this case the residual deviance and Pearson goodness-of fit statistics are determined entirely by the fitted values. This means that there is no concept of residual variability, and goodness-of-fit tests are not meaningful."
I don't understand why that is. Does anyone understand?