Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

The aim of this study was to examine the precision of item parameter estimation in different sample sizes and test lengths under three parameter logistic model (3PL) item response theory (IRT) model, where the trait measured by a test was not normally distributed or had a skewed distribution. In the study, number of categories (1-0), and item…

Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious…

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

The nominal response model (NRM), a much understudied polytomous item response theory (IRT) model, provides researchers the unique opportunity to evaluate within-item category distinctions. Polytomous IRT models, such as the NRM, are frequently applied to psychological assessments representing constructs that are unlikely to be normally…

When studying differential item functioning (DIF) with students with disabilities (SWD) focal groups typically suffer from small sample size, whereas the reference group population is usually large. This makes it possible for a researcher to select a sample from the reference population to be similar to the focal group on the ability scale. Doing…

The purpose of this study was to explore the degree of grain size of the attributes and the sample sizes that can support accurate parameter recovery with the General Diagnostic Model (GDM) for a large-scale international assessment. In this resampling study, bootstrap samples were obtained from the 2003 Grade 8 TIMSS in Mathematics at varying…

A simulation study was conducted to explore the performance of the linear logistic test model (LLTM) when the relationships between items and cognitive components were misspecified. Factors manipulated included percent of misspecification (0%, 1%, 5%, 10%, and 15%), form of misspecification (under-specification, balanced misspecification, and…

This paper compares three methods of item calibration--concurrent calibration, separate calibration with linking, and fixed item parameter calibration--that are frequently used for linking item parameters to a base scale. Concurrent and separate calibrations were implemented using BILOG-MG. The Stocking and Lord (1983) characteristic curve method…

Investigates the BILOG computer program's ability to recover known item parameters for different numbers of items, examinees, and variances of the prior distributions of discrimination parameters for the two-parameter logistic item-response theory model. For samples of at least 250 examinees and 15 items, simulation results support using BILOG.…

The feasibility of quick norms derived by the procedure described by B. D. Wright and M. H. Stone (1979) was investigated. Norming differences between traditionally calculated means and Rasch "quick" means were examined for simulated data sets of varying sample size, test length, and type of distribution. A 5 by 5 by 2 design with a…

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…

Responses to previously calibrated items administered in a computerized adaptive testing (CAT) mode may be used to recalibrate the items. This live-data simulation study investigated the possibility, and limitations, of on-line adaptive recalibration of precalibrated items. Responses to items of a Rasch-based paper-and-pencil licensure examination…