ABSTRACT
Incidental parameters are very commonly encountered in Item Response Theory, although in many applications it is easy to quarrel with the idea that the incidental parameters are not themselves of interest. In the statistical and econometric literature, it is common to find discussions of probability models in which some parameters are of direct interest but others are nuisance parameters that are not of direct interest but affect the distribution of the observations. Conditional estimation, which employs conditional maximum likelihood, avoids the inconsistency problems of joint estimation, but there can be a significant computational cost. Thus, unrestricted marginal estimation applies to the generalized partial credit model and to the additive model for nominal responses, but it is not useful for the generalized partial credit model.
