One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another, irrespective of true group-mean differences on the constructs being measured. This article is focused on item response theory based likelihood ratio testing for DIF (IRT-LR or…

Pseudo-Bayesian and joint maximum likelihood procedures were compared for their ability to estimate item parameters for item response theory's (IRT's) three-parameter logistic model. Item responses were generated for sample sizes of 2,000 and 500; test lengths of 35 and 15; and examinees of high, medium, and low ability. (TJH)