Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

The product Bayes factor (PBF) synthesizes evidence for an informative hypothesis across heterogeneous replication studies. It can be used when fixed- or random effects meta-analysis fall short. For example, when effect sizes are incomparable and cannot be pooled, or when studies diverge significantly in the populations, study designs, and…

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons…

Skill prerequisite information is useful for tutoring systems that assess student knowledge or that provide remediation. These systems often encode prerequisites as graphs designed by subject matter experts in a costly and time-consuming process. In this paper, we introduce "Combined student Modeling and prerequisite Discovery"…

BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

Intelligent behavior of adaptive educational systems is based on student models. Most research in student modeling focuses on student learning (acquisition of skills). We focus on prior knowledge, which gets much less attention in modeling and yet can be highly varied and have important consequences for the use of educational systems. We describe…

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

As an assessment method based on a constructivist approach, peer assessment has become popular in recent years. However, in peer assessment, a problem remains that reliability depends on the rater characteristics. For this reason, some item response models that incorporate rater parameters have been proposed. Those models are expected to improve…

This paper describes and evaluates the use of measurement decision theory (MDT) to classify examinees based on their item response patterns. The model has a simple framework that starts with the conditional probabilities of examinees in each category or mastery state responding correctly to each item. The presented evaluation investigates: (1) the…