Although the generalized deterministic inputs, noisy "and" gate model (G-DINA; de la Torre, 2011) is a general cognitive diagnosis model (CDM), it does not account for the heterogeneity that is rooted from the existing latent groups in the population of examinees. To address this, this study proposes the mixture G-DINA model, a CDM that…

Large language models (LLMs) are increasingly adopted in educational contexts to provide personalized support to students and teachers. The unprecedented capacity of LLM-based applications to understand and generate natural language can potentially improve instructional effectiveness and learning outcomes, but the integration of LLMs in education…

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…

Since 2018, institutions of higher education have been aware of the "enrollment cliff" which refers to expected declines in future enrollment. This paper attempts to describe how prepared institutions in Ohio are for this future by looking at trends leading up to the anticipated decline. Using IPEDS data from 2012-2022, we analyze trends…

Dynamic Item Response Models extend the standard Item Response Theory (IRT) to capture temporal dynamics in learner ability. While these models have the potential to allow instructional systems to actively monitor the evolution of learner proficiency in real time, existing dynamic item response models rely on expensive inference algorithms that…

Machine learning (ML) has become commonplace in educational research and science education research, especially to support assessment efforts. Such applications of machine learning have shown their promise in replicating and scaling human-driven codes of students' work. Despite this promise, we and other scholars argue that machine learning has…

Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

This paper develops a spreadsheet simulation methodology for teaching simulation and performance analysis of priority queues with multiple servers, without resorting to macros, add-ins, or array formula. The approach is made possible by a "single overtaking" simplifying assumption under which any lower-priority customer may be passed in…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

To prevent students from learning risks and improve teachers' teaching quality, it is of great significance to provide accurate early warning of learning performance to students by analyzing their interactions through an e-learning system. In existing research, the correlations between learning risks and students' changing cognitive abilities or…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

The emergence of online learning has sparked increased interest in predicting learners' academic performance to enhance teaching effectiveness and personalized learning. In this context, we propose a complex model APPMLT-CBT which aims to predict learners' performance in online learning settings. This systemic model integrates cognitive, social,…

The TETRAD for constraint-based aids to causal model specification project and related work in computer science aims to apply standards of rigor and precision to the problem of using data and background knowledge to make inferences about a model's specifications. Several algorithms that are implemented in the TETRAD II program are presented. (SLD)