I know sometimes I want to know the population-level estimates, but the problem with GEEs is I can't calculate the likelihood, and therefore all models I make with it aren't comparable, and I don't know which model is right. For all I know what I am fitting with GEEs could be the noise rather than the true value. If models are specified differently, the entire conclusions can be different. There's Quasi-likelihood but I can't compare the quasi-likelihood to a chi-square distribution and do likelihood ratio tests with it.
Someone told me that GEEs are interpreted in the case of drug trials as if I were to give the entire population (all the people) many of whom are not sick, the drug, what kind of effect we would see.
But that would be stupid unless we're measuring clinical phase 1 trials, testing the toxicity on a generally healthy population.
Under no case would you ever want to give the drug to the entire population( that's impossible and useless and never going to happen). So why use a model that estimates what would happen if we did give the treatment to everyone on earth, the universe, and beyond?
I disagree with the contention that no model is correct; I believe there is an objectively correct model. To say no model is better than the other is to misunderstand or reject the validity of maximum likelihood and all good modeling metrics.
Why use GEEs?
I heard it's like the difference between public health and individual health. But why are the estimates of individual effects so different from population-level effects when individuals are supposed to be representative of the population level?