ABSTRACT
This chapter presents item response theory (IRT) methodologies applicable to multistage tests (MSTs), focusing on two components necessary for MST administration: routing and scoring. Some basic assumptions that will be made here are as follows: (1) an item response model determines the probability of observing response Xj = xj for an item j given a value of the latent trait θ and (2) item responses are conditionally independent given the latent trait. For simplicity in exposition, it will further be assumed that (3) the latent trait is unidimensional, (4) responses are categorical, and (5) the item response function is defined by a set of item parameters and the latent trait. In the following, it is assumed that item parameters have been estimated in advance and that an MST being considered for administration has already been assembled. For information regarding MST assembly, see van der Linden and Diao; Han and Guo; Zheng, Wang, Culbertson, and Chang; and Verschoor and Eggen, this volume.
