Research suggests that generative AI (GAI) responds to divergent thinking (DT) prompts with multiple ideas, some of which seem to be original. The present investigation administered 55 DT tasks to three GAI services (Bard, GPT 3.5, and GPT 4.0). Instead of examining individual responses, an Idea Density algorithm was used to assess the output.…

Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and…

Researchers tasked with understanding the effects of educational technology innovations face the challenge of providing evidence of causality. Given the complexities of studying learning in authentic contexts interwoven with technological affordances, conducting tightly-controlled randomized experiments is not always feasible nor desirable. Today,…

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and…

Intensive longitudinal data has been widely used to examine reciprocal or causal relations between variables. However, these variables may not be temporally aligned. This study examined the consequences and solutions of the problem of temporal misalignment in intensive longitudinal data based on dynamic structural equation models. First the impact…

Generalized structured component analysis (GSCA) is a multivariate method for specifying and examining interrelationships between observed variables and components. Despite its data-analytic flexibility honed over the decade, GSCA always defines every component as a linear function of observed variables, which can be less optimal when observed…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by…

The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In…

The present work focuses on the performance of two types of shrinkage priors--the horseshoe prior and the recently developed regularized horseshoe prior--in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold…

This research explores the process of a Participatory Research (PR) project that brought together university researchers with museum practitioners to create reflective tools that can be used to better understand real practical challenges. This project followed Bourke's (2009) definition of PR, viewing the process as a collaborative endeavour…

As learning analytics use grows across U.S. colleges and universities, so does the need to discuss the plans, purposes, and paths for the data collected via learning analytics. More specifically, students, faculty, and others who are impacted by learning analytics use should have more information about their campus' learning analytics practices…

Knowledge integration remains, paradoxically, both a key methodology and an elusive mystery in crossdisciplinary work such as interdisciplinary studies, team science, and transdisciplinary research. Many case studies have described compound events and iterations leading to remarkable integrative achievements. Even though a wealth of work on…

Understanding software modelers' difficulties and evaluating their performance is crucial to Model-Driven Engineering (MDE) education. The software modeling process contains fine-grained information about the modelers' analysis and thought processes. However, existing research primarily focuses on identifying obvious issues in the software…

Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…