Large-scale education data are collected via complex sampling designs that incorporate clustering and unequal probability of selection. Multilevel models are often utilized to account for clustering effects. The probability weighted approach (PWA) has been frequently used to deal with the unequal probability of selection. In this study, we examine…

Bayesian knowledge tracing model (BKT) is a typical student knowledge assessment method. It is widely used in intelligent tutoring systems. In the standard BKT model, all knowledge and skills are independent of each other. However, in the process of student learning, they have a very close relation. A student may understand knowledge B better when…

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…

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…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

We propose a method of generating teaching policies for use in intelligent tutoring systems (ITS) for concept learning tasks [1], e.g., teaching students the meanings of words by showing images that exemplify their meanings à la Rosetta Stone [2] and Duo Lingo [3]. The approach is grounded in control theory and capitalizes on recent work by [4],…

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

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…

Studies of psychological distress (PD) in university students have shown that they have high prevalence rates. These findings have raised concerns that PD may be leading to poorer student outcomes, such as elevated dropout rates. The aim of this study was to examine the association of PD in undergraduate university students with the competing…

Bayesian Knowledge Tracing (BKT) has been in wide use for modeling student skill acquisition in Intelligent Tutoring Systems (ITS). BKT tracks and updates student's latent mastery of a skill as a probability distribution of a binary variable. BKT does so by accounting for observed student successes in applying the skill correctly, where success is…

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…

Interactive learning environments with body-centric technologies lie at the intersection of the design of embodied learning activities and multimodal learning analytics. Sensing technologies can generate large amounts of fine-grained data automatically captured from student movements. Researchers can use these fine-grained data to create a…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

Additive Factors Model (AFM) and Performance Factors Analysis (PFA) are two popular models of student learning that employ logistic regression to estimate parameters and predict performance. This is in contrast to Bayesian Knowledge Tracing (BKT) which uses a Hidden Markov Model formalism. While all three models tend to make similar predictions,…