The testlet design is very popular in educational and psychological assessments. This article proposes a new cognitive diagnosis model, the multiple-choice cognitive diagnostic testlet (MC-CDT) model for tests using testlets consisting of MC items. The MC-CDT model uses the original examinees' responses to MC items instead of dichotomously scored…

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 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…

Application of MIRT modeling procedures is dependent on the quality of parameter estimates provided by the estimation software and techniques used. This study investigated model parameter recovery of two popular MIRT packages, BMIRT and flexMIRT, under some common measurement conditions. These packages were specifically selected to investigate the…

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…

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)…

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…