Identifying DIF for Latent Classes with the Dirichlet Process

of the Dissertation Identifying DIF for Latent Classes with the Dirichlet Process by Miles Satori Chen Doctor of Philosophy in Statistics University of California, Los Angeles, 2015 Professor Peter Bentler, Chair In Item Response Theory (IRT), Differential Item Functioning (DIF) occurs when individuals who have the same ability, but belong to different groups, have different probabilities of answering an item correctly. Traditional DIF methods require that the grouping variable be observable, like gender or ethnicity. Latent class IRT, on the other hand, allows for the fitting of IRT models where the grouping variable is unobserved. Current latent class IRT methods (e.g. mixed Rasch models) require that the number of mixing components be defined in the estimation process. This dissertation proposes two latent class models, each with a Markov chain Monte Carlo algorithm, that can be used to fit IRT data without the need to specify the number of latent classes. The models employ a Dirichlet process or stick-breaking prior to allow an undefined number of mixing components to be fit. Simulation results indicate that the models can correctly identify the latent classes without the need to specify how many unobserved groups there are. The power to correctly detect multiple latent classes, however, is quite low especially if the amount of DIF is small or if only a few items in a test exhibit DIF. The results of the proposed models are compared to those of the mixed Rasch model.