This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE)…

This paper describes how item response theory (IRT) methods of test-equating could be applied to the maintenance of public examination standards in England. IRT methods of test-equating have been sparingly applied to the main public examinations in England, namely the General Certificate of Secondary Education (GCSE), the equivalent of a school…

This study gathered, analyzed, and compared perspectives of students who were honors-eligible but never began the program, students who began in honors and discontinued their enrollment, and those who were persisting in honors. Broadly speaking (and not surprisingly), the responses of students persisting in honors reflected the most positive…

Nonlinear multilevel latent variable modeling has been suggested as an alternative to traditional hierarchical linear modeling to more properly handle measurement error and sampling error issues in contextual effects modeling. However, a nonlinear multilevel latent variable model requires significant computational effort because the estimation…

Understanding students' intentions to study science at upper-secondary school, at university, and to follow science careers continues as a central concern for international science education. Prior research has highlighted that students' science confidence has been associated with their intentions to study science further, although…

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

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…

This study elaborates the Rasch differential item functioning (DIF) model formulation under the marginal maximum likelihood estimation context. Also, the Rasch DIF model performance was examined and compared with the Mantel-Haenszel (MH) procedure in small sample and short test length conditions through simulations. The theoretically known…

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach.…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Incomplete nonnormal data are common occurrences in applied research. Although these 2 problems are often dealt with separately by methodologists, they often cooccur. Very little has been written about statistics appropriate for evaluating models with such data. This article extends several existing statistics for complete nonnormal data to…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…

Davidian-curve item response theory (DC-IRT) is introduced, evaluated with simulations, and illustrated using data from the Schedule for Nonadaptive and Adaptive Personality Entitlement scale. DC-IRT is a method for fitting unidimensional IRT models with maximum marginal likelihood estimation, in which the latent density is estimated,…

Three statistical testing procedures well-known in the maximum likelihood approach are the Wald, likelihood ratio (LR), and score tests. Although well-known, the application of these three testing procedures in the logistic regression method to investigate differential item function (DIF) has not been rigorously made yet. Employing a variety of…