Two fundamental steps in item response theory (IRT) analysis are those of parameter estimation and diagnostics. Regarding the main estimation methods, we have already provided a summary description in Section 3.7 with reference to IRT models for dichotomous items. We recall that the most well-known estimation strategies are based on the joint maximum likelihood (JML) method, on the conditional maximum likelihood (CML) method, and on the marginal maximum likelihood (MML) method. The first two methods rely on the so-called fixed-effects formulation of the model, in which a fixed parameter is used to represent the latent trait level of every sample unit. On the other hand, the MML method relies on the random-effects formulation that assumes that each of these individual levels is a realization of a latent variable, the distribution of which may be continuous or discrete. These methods have different advantages and disadvantages and a different degree of applicability.