The subject of this dissertation is the examination of differential item functioning (DIF) through the use of loglinear Rasch models with latent classes. DIF refers to the probability that a correct response among equally able test takers is different for various racial, ethnic, and gender groups. Because usual methods of detecting DIF give little information about the reason an item is biased, use of the solution-error response-error (SERE) model of H. Kelderman is proposed. It is demonstrated that the SERE model can show whether DIF is caused by the difficulty of the item, the attractiveness of its alternatives, or both. The large amount of computer memory space required makes this method impractical for a large number of items. A new method is proposed based on the division of the whole item set into several subsets, which is made possible by the collapsibility of the SERE model. With the use of subsets of items, the parameters of the entire SERE model can be obtained only by simultaneous estimation of the parameters of the collapsed SERE models through use of pseudo-likelihood theory. A simulation study demonstrates that a distinction can be made between the two types of DIF using the new approach. A generalization of the SERE model applicable to polytomously scored latent states, that may be explained with a multidimensional latent space, is discussed. Five appendices illustrate applications of these models with reference to existing tests and the collapsed SERE model. (Contains 167 references.) (SLD)