The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

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…

The present study presents the formulation of graded response models in the multilevel framework (as nonlinear mixed models) and demonstrates their use in estimating item parameters and investigating the group-level effects for specific covariates using Bayesian estimation. The graded response multilevel model (GRMM) combines the formulation of…

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

The effects of a multidimensional latent trait space on estimation of item and person parameters by the computer program LOGIST are examined. Several item pools were simulated that ranged from truly unidimensional to an inconsequential general latent trait. Item pools with intermediate levels of prepotency of the general latent trait were also…

This paper reviews the basic elements of the EM approach to estimating item parameters and illustrates its use with one simulated and one real data set. In order to illustrate the use of the BILOG computer program, runs for 1-, 2-, and 3-parameter models are presented for the two sets of data. First is a set of responses from 1,000 persons to five…

This study investigated the construct validity of the revised Special Education-Mental Handicaps Georgia Teacher Certification Test (MH-TCT) using hierarchical confirmatory factor analysis and LISREL VI. The primary objective was to determine whether first-order and second-order factors correspond to item/objective/test relationships defined by…