Files
Abstract
Mixture IRT models have been applied to investigate the latent groups that exist in the respondent population and how the same set of test items function differently for different latent groups. However, they assume that a respondent remains in the same latent group across test items, which can be unreasonable in certain scenarios. In this dissertation, a mixed membership Rasch model (MMR) is developed to help overcome this limitation in mixture IRT models. The MMR is built by integrating the Rasch model into the framework of mixed membership models which are considered as a soft clustering technique. In the MMR, a respondent belongs to all the latent groups but with different probabilities at the test level. At the item level, a respondent belongs to only one of the latent groups in each test item and the latent group to which he or she belongs can be different across items. For a response to an item, the probability of a correct answer is parameterized using the Rasch model and the item difficulties in the Rasch model are assumed to vary with latent groups. The MMR is estimated using a Metropolis-within-Gibbs algorithm. This dissertation includes three simulation studies. In Study I, parameter recovery of the MMR is investigated given different test conditions and different priors used in the Metropolis-within-Gibbs algorithm, when the item difficulties across latent groups are known. The design and the purpose of Study II are similar to those in Study I except that in Study II, item difficulties across latent groups are unknown and thus also need to be estimated. In order to run the MMR, the number of latent groups has to be specified even though it is typically unknown. Selecting the best fitting model from among candidate models is an important part of modeling with an MMR. Therefore, in Study III, the performance of several widely applied information criteria is examined in different test conditions in term of their accuracy in selecting the best fitting MMR.