I am taking two courses where I learn GMM and MNL separately. However, I do see some similarities between they two: like we need indicator variable for discrete choice modeling when using the MLE, while we also need the categorical variable for estimation mean/variance/weight for GMM using the E-M algorithm. My problem is how to intuitively understand why we cannot only use MLE to estimate the parameters of GMM? Like MLE is a method of finding the set of population parameters that produce observed sample most often. Some tutorials that I am referring to are : (1) discrete choice model http://www.tcd.ie/civileng/Staff/Brian.Caulfield/T2%20-%20Transport%20Modelling/Discrete%20Choice%20Modelling.pdf (2)GMM http://www.idiap.ch/~fleuret/files/EE613/EE613-slides-4.pdf
Thanks in advance!