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…

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…

Educational Data Mining is an emerging discipline which seeks to develop methods to explore large amounts of data from educational settings, in order to understand students' behavior, interests and results in a better way. In recent years there have been various works related to this specialty and multiple data mining techniques derived from this…

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…

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…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

Simulation or game-based assessments produce outcome data and process data. In this article, some statistical models that can potentially be used to analyze data from simulation or game-based assessments are introduced. Specifically, cognitive diagnostic models that can be used to estimate latent skills from outcome data so as to scale these…

In educational technology and learning sciences, there are multiple uses for a predictive model of whether a student will perform a task correctly or not. For example, an intelligent tutoring system may use such a model to estimate whether or not a student has mastered a skill. We analyze the significance of data recency in making such…

As expectations of the economic impact of educational attainment are soaring (Hanushek & Woessmann, 2009) and conjectures about successful national educational reforms (Mourshed, Chijioke, & Barber, 2010) are welcomed by educational policy-makers in many countries, a careful assessment of the empirical evidence for these kinds of claims is…

"Growth mixture models" (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class…

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

Sample size ranks as one of the most important factors that affect the item calibration task. However, due to practical concerns (e.g., item exposure) items are typically calibrated with much smaller samples than what is desired. To address the need for a more flexible framework that can be used in small sample item calibration, this article…

Assessments consisting of different domains (e.g., content areas, objectives) are typically multidimensional in nature but are commonly assumed to be unidimensional for estimation purposes. The different domains of these assessments are further treated as multi-unidimensional tests for the purpose of obtaining diagnostic information. However, when…

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993)and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT…