The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

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 effects of mean ability difference (MAD) and short tests on the performance of various DIF methods have been studied extensively in previous simulation studies. Their effects, however, have not been studied under multilevel data structure. MAD was frequently observed in large-scale cross-country comparison studies where the primary sampling…

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

This study aimed to investigate the effects of calibration sample size and item bank size on examinee ability estimation in computerized adaptive testing (CAT). For this purpose, a 500-item bank pre-calibrated using the three-parameter logistic model with 10,000 examinees was simulated. Calibration samples of varying sizes (150, 250, 350, 500,…

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

Testlets, or groups of related items, are commonly included in educational assessments due to their many logistical and conceptual advantages. Despite their advantages, testlets introduce complications into the theory and practice of educational measurement. Responses to items within a testlet tend to be correlated even after controlling for…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

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…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…