Among current state-of-art estimation methods for multilevel IRT models, the two-stage divide-and-conquer strategy has practical advantages, such as clearer definition of factors, convenience for secondary data analysis, convenience for model calibration and fit evaluation, and avoidance of improper solutions. However, various studies have shown…

One of the highest ambitions in educational technology is the move towards personalized learning. To this end, computerized adaptive learning (CAL) systems are developed. A popular method to track the development of student ability and item difficulty, in CAL systems, is the Elo Rating System (ERS). The ERS allows for dynamic model parameters by…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

Because of concerns about test security, different test forms are typically used across different testing occasions. As a result, equating is necessary in order to get scores from the different test forms that can be used interchangeably. In order to assure the quality of equating, multiple equating methods are often examined. Various equity…

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests…

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

The capacity of Bayesian methods in estimating complex statistical models is undeniable. Bayesian data analysis is seen as having a range of advantages, such as an intuitive probabilistic interpretation of the parameters of interest, the efficient incorporation of prior information to empirical data analysis, model averaging and model selection.…

Results from two Monte Carlo studies in item response theory (comparisons of computer item analysis programs and Bayes estimation procedures) are analyzed with inferential methods to illustrate the procedures' strengths. It is recommended that researchers in item response theory use both descriptive and inferential methods to analyze Monte Carlo…

Diagnostic score reports linking assessment outcomes to instructional interventions are one of the most requested features of assessment products. There is a body of interesting work done in the last 20 years including Tatsuoka's rule space method (Tatsuoka, 1983), Haertal and Wiley's binary skills model (Haertal, 1984; Haertal & Wiley, 1993),…