Abstract

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 (Hotelling, 1940) that are not of direct interest but affect the distribution of the observations (Cox and Hinkley, 1974, p. 35). It is also common to encounter cases in which some parameters are deemed structural parameters and some parameters are deemed incidental parameters. Typically, the incidental parameters are treated as nuisance parameters. The structural parameters are regarded as parameters of direct interest. The incidental parameters are regarded as parameters not directly of interest that are associated with individual observations (Neyman and Scott, 1948). The inferential challenge that is relevant to IRT arises when the number of nuisance parameters increases as the number of observations increases.