Online collaborative discussion (OCD) focuses on promoting individual knowledge inquiry and group knowledge construction through active peer interactions and communications. In practice, it is necessary to explore how different modes of OCD come into play, in which student engagement can function as an evaluating indicator. To identify student…

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

Although educational research and evaluation generally occur in multilevel settings, many analyses ignore cluster effects. Neglecting the nature of data from educational settings, especially in non-randomized experiments, can result in biased estimates with long-term consequences. Our manuscript improves the availability and understanding of…

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the…

This paper introduces an approach that uses latent class analysis to identify cut scores (LCA-CS) and categorize respondents based on context scales derived from largescale assessments like PIRLS, TIMSS, and NAEP. Context scales use Likert scale items to measure latent constructs of interest and classify respondents into meaningful ordered…

We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

In this article, we outline several activities revolving around soccer players who participated in the 2018 FIFA World Cup and 2019 FIFA Women's World Cup. Classroom activities are described from different perspectives, useful for a range of different statistics courses. In a first semester probability theory course, students investigate the…

Educational stakeholders are keen to know the magnitude and importance of different interventions. However, the way evidence is communicated to support understanding of the effectiveness of an intervention is controversial. Typically studies in education have used the standardised mean difference as a measure of the impact of interventions. This…