A learner model reflects learning patterns and characteristics of a learner. A learner model with learning history and its effectiveness plays a significant role in supporting a learner's understanding of their strengths and weaknesses of their way of learning in order to make proper adjustments for improvement. Nowadays, learners have been…

The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee's ability and optimally…

Given the questionnaire design and the nature of the problem, partially ordered data that are neither completely ordered nor completely unordered are frequently encountered in social, behavioral, and medical studies. However, early developments in partially ordered data analysis are very limited and restricted only to cross-sectional data. In this…

Knowledge tracing algorithms such as Bayesian Knowledge Tracing (BKT) can provide students and teachers with helpful information about their progress towards learning objectives. Despite the popularity of BKT in the research community, the algorithm is not widely adopted in educational practice. This may be due to skepticism from users and…

Digitalization and automation of test administration, score reporting, and feedback provision have the potential to benefit large-scale and formative assessments. Many studies on automated essay scoring (AES) and feedback generation systems were published in the last decade, but few connected AES and feedback generation within a unified framework.…

The adaptive learning problem concerns how to create an individualized learning plan (also referred to as a learning policy) that chooses the most appropriate learning materials based on a learner's latent traits. In this article, we study an important yet less-addressed adaptive learning problem--one that assumes continuous latent traits.…

Response time models (RTMs) are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular RTMs. Several existing statistics for testing normality and the fit of factor analysis models are repurposed for testing the fit of the lognormal model. A…

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain…

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…

Equating and scaling in the context of small sample exams, such as credentialing exams for highly specialized professions, has received increased attention in recent research. Investigators have proposed a variety of both classical and Rasch-based approaches to the problem. This study attempts to extend past research by (1) directly comparing…

Response-time models are of increasing interest in educational and psychological testing. This paper focuses on the lognormal model for response times (van der Linden, 2006), which is one of the most popular response-time models. Several existing statistics for testing normality and the fit of factor-analysis models are repurposed for testing the…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

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…

When selecting a multilevel model to fit to a dataset, it is important to choose both a model that best matches characteristics of the data's structure, but also to include the appropriate fixed and random effects parameters. For example, when researchers analyze clustered data (e.g., students nested within schools), the multilevel model can be…

This article presents a new approach to the analysis of how students answer tests and how they allocate resources in terms of time on task and revisiting previously answered questions. Previous research has shown that in high-stakes assessments, most test takers do not end the testing session early, but rather spend all of the time they were…