This paper attempts to bridge the gap between classical test theory and item response theory. It is demonstrated that the familiar and popular statistics used in classical test theory can be translated into a Bayesian framework where all of the advantages of the Bayesian paradigm can be realized. In particular, prior opinion can be introduced and…

Student misconceptions have been studied for decades from a curricular/instructional perspective and from the assessment/test level perspective. Numerous misconception assessment tools have been developed in order to measure students' misconceptions relative to the correct content. Often, these tools are used to make a variety of educational…

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

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…

Large-scale experiments are often expensive and time consuming. Although Massive Online Open Courses (MOOCs) provide a solid and consistent framework for learning analytics, MOOC practitioners are still reluctant to risk resources in experiments. In this study, we suggest a methodology for simulating MOOC students, which allow estimation of…

Computer-based scaffolding plays a pivotal role in improving students' higher-order skills in the context of problem-based learning for Science, Technology, Engineering and Mathematics (STEM) education. The effectiveness of computer-based scaffolding has been demonstrated through traditional meta-analyses. However, traditional meta-analyses suffer…

Although ownership is acknowledged to exert a potent influence on various aspects of information processing, the origin of these effects remains largely unknown. Based on the demonstration that self-relevance facilitates perceptual judgments (i.e., the self-prioritization effect), here we explored the possibility that ownership enhances object…

A family of learning models that integrates a cognitive diagnostic model and a higher-order, hidden Markov model in one framework is proposed. This new framework includes covariates to model skill transition in the learning environment. A Bayesian formulation is adopted to estimate parameters from a learning model. The developed methods are…

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are…

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

The future of education is human expertise and artificial intelligence working in conjunction, a revolution that will change the education as we know it. The Intelligent Tutoring System is a key component of this future. A quantitative measurement of efficacies of practice to heterogeneous learners is the cornerstone of building an effective…

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (?"Levels") model and a model involving a quadratic function…

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…

The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance…