Consider a response y and data matrix X. Suppose I'm creating a model of the form -
y ~ g(X,$\theta$)
(g() could be any function of X and $\theta$)
Now, for estimating $\theta$ using Maximum Likelihood (ML) method, I could go ahead either with Conditional ML (assuming I know the form of conditional density f(y|X) ) or with Joint ML (assuming I know the form of joint density f(y,X) or equivalently, f(X|y) * f(y) )
I was wondering if there are any considerations in going ahead with either of the above two methods apart from the assumption about the densities. Also, are there any instances (specific types of data) where one method overpowers other most of the time?