Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

Maintaining and cultivating student engagement is critical for learning. Understanding factors affecting student engagement can help in designing better courses and improving student retention. The large number of participants in massive open online courses (MOOCs) and data collected from their interactions on the MOOC open up avenues for studying…

Higher education in America is characterized by widespread access to college but low rates of completion, especially among undergraduates at less selective institutions. We analyze longitudinal transcript data to examine processes leading to graduation, using Hidden Markov modeling. We identify several latent states that are associated with…

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

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…

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…

Participatory sensing is a data collection method in which communities of people collect and share data to investigate large-scale processes. These data have many features often associated with the big data paradigm: they are rich and multivariate, include non-numeric data, and are collected as determined by an algorithm rather than by traditional…

Social networks in education commonly involve some form of grouping, such as friendship cliques or teacher departments, and blockmodels are a type of statistical social network model that accommodate these grouping or blocks by assuming different within-group tie probabilities than between-group tie probabilities. We describe a class of models,…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…

Latent transition analysis (LTA) was initially developed to provide a means of measuring change in dynamic latent variables. In this article, we illustrate the use of a cognitive diagnostic model, the DINA model, as the measurement model in a LTA, thereby demonstrating a means of analyzing change in cognitive skills over time. An example is…

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 focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from…

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,…

The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…

The Pinyin Tutor has been used the past few years at over thirty institutions around the world to teach students to transcribe spoken Chinese phrases into Pinyin. Large amounts of data have been collected from this program on the types of errors students make on this task. We analyze these data to discover what makes this task difficult and use…