Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

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…