Knowledge tracing algorithms such as Bayesian Knowledge Tracing (BKT) can provide students and teachers with helpful information about their progress towards learning objectives. Despite the popularity of BKT in the research community, the algorithm is not widely adopted in educational practice. This may be due to skepticism from users and…

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…

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…

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…

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,…

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

Plausible values can be used to either estimate population-level statistics or compute point estimates of latent variables. While it is well known that five plausible values are usually sufficient for accurate estimation of population-level statistics in large-scale surveys, the minimum number of plausible values needed to obtain accurate latent…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…

One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…

Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…

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…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…