The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee's ability and optimally…

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

The present study investigates different approaches to adding covariates and the impact in fitting mixture item response theory models. Mixture item response theory models serve as an important methodology for tackling several psychometric issues in test development, including the detection of latent differential item functioning. A Monte Carlo…

The applications of item response theory (IRT) models assume local item independence and that examinees are independent of each other. When a representative sample for psychometric analysis is selected using a cluster sampling method in a testlet-based assessment, both local item dependence and local person dependence are likely to be induced.…

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as…

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte…

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of…

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…