Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

Examines the ways in which level-1 outliers can impact the estimation of fixed effects and random effects in hierarchical models (HMs). Also outlines and illustrates the use of Markov Chain Monte Carlo algorithms for conducting sensitivity analyses under "t" level-1 assumptions, including algorithms for settings in which the degrees of…

Illustrates that sampling variance can be very large when a three-wave quasi simplex model is used to obtain reliability estimates. Also shows that, for the reliability parameter to be identified, the model assumes a Markov process. These problems are evaluated with both real and Monte Carlo data. (SLD)

A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel…

In some areas of measurement item parameters should not be modeled as fixed but as random. Examples of such areas are: item sampling, computerized item generation, measurement with substantial estimation error in the item parameter estimates, and grouping of items under a common stimulus or in a common context. A hierarchical version of the…

The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal…

Introduces a new technique for estimating the parameters of models with continuous latent data. To streamline presentation of this Markov Chain Monte Carlo (MCMC) method, the Rasch model is used. Also introduces a new sampling-based Bayesian technique, the DA-T-Gibbs sampler. (SLD)

In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and…

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple…

Examined the accuracy of the Gibbs sampling Markov chain Monte Carlo procedure for estimating item and person (theta) parameters in the one-parameter logistic model. Analyzed four empirical datasets using the Gibbs sampling, conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood methods. Discusses the conditions…

Developed an item response model for characterizing test-compromise that enables the estimation of item preview and score-gain distributions. In the approach, models parameters and posterior distributions are estimated by Markov Chain Monte Carlo procedures. Simulation study results suggest that when at least some test items are known to be…

The accuracy of the Markov chain Monte Carlo procedure, Gibbs sampling, was considered for estimation of item and ability parameters of the one-parameter logistic model. Four data sets were analyzed to evaluate the Gibbs sampling procedure. Data sets were also analyzed using methods of conditional maximum likelihood, marginal maximum likelihood,…

For complex educational assessments, there is an increasing use of "item families," which are groups of related items. However, calibration or scoring for such an assessment requires fitting models that take into account the dependence structure inherent among the items that belong to the same item family. C. Glas and W. van der Linden…

This paper explores the application of a technique for hierarchical item response theory (IRT) calibration of complex constructed response tasks that has promise both as a calibration tool and as a means of evaluating the isomorphic equivalence of complex constructed response tasks. Isomorphic tasks are explicitly and rigorously designed to be…