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…

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain…

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their…

Equating and scaling in the context of small sample exams, such as credentialing exams for highly specialized professions, has received increased attention in recent research. Investigators have proposed a variety of both classical and Rasch-based approaches to the problem. This study attempts to extend past research by (1) directly comparing…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

In the era of artificial intelligence (AI), big data (BD), and digital transformation (DT), analytics students should gain the ability to solve business problems by integrating various methods. This teaching brief illustrates how two such methods--Bayesian analysis and Markov chains--can be combined to enhance student learning using the Analytics…

This article presents a new approach to the analysis of how students answer tests and how they allocate resources in terms of time on task and revisiting previously answered questions. Previous research has shown that in high-stakes assessments, most test takers do not end the testing session early, but rather spend all of the time they were…

Immediacy is one of the necessary criteria to show strong evidence of treatment effect in single case experimental designs (SCEDs). With the exception of Natesan and Hedges (2017) no inferential statistical tool has been used to demonstrate or quantify it until now. We investigate and quantify immediacy by treating the change-points between the…

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard good-ness-of-fit statistics. Limited-information fit…

Intelligent tutoring systems (ITSs) teach skills using learning-by-doing principles and provide learners with individualized feedback and materials adapted to their level of understanding. Given a learner's history of past interactions with an ITS, a learner performance model estimates the current state of a learner's knowledge and predicts her…

In this article, we systematically introduce the just another Gibbs sampler (JAGS) software program to fit common Bayesian cognitive diagnosis models (CDMs) including the deterministic inputs, noisy "and" gate model; the deterministic inputs, noisy "or" gate model; the linear logistic model; the reduced reparameterized unified…

A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on…

Severity and centrality are two main kinds of rater effects posing threats to the validity and fairness of performance assessments. Adopting Jin and Wang's (2018) extended facets modeling approach, we separately estimated the magnitude of rater severity and centrality effects in the web-based TestDaF (Test of German as a Foreign Language) writing…

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…