The models and procedures discussed in this paper are related to those presented in Bock and Aitkin (1981), where they considered the 2-parameter probit model and approximated a normally distributed prior distribution of abilities by a finite and discrete distribution. One purpose of this paper is to clarify the nature of the general EM (GEM) solution, assuming that convergence has already taken place. For this purpose the general situation is considered and conditions are then given under which the GEM solution maximizes the likelihood function based on incomplete data. For the 2-parameter logistic model, the equations occurring at each iteration of the GEM algorithm are compared with the likelihood equations for the incomplete data. The GEM approach is shown as computationally simpler than the solution via direct methods. In practice, for latent trait applications in particular, once there is convergence, the author feels it is usually easy to test the solution by examining the likelihood function in a neighborhood of the solution and to verify whether it is at least a local maximum. This paper concludes by demonstrating that for the one parameter logistic model, convergence by the concavity of the log-likelihood function is assured. (PN)