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Posterior Predictive Model Checking (PPMC) is frequently used for model fit evaluation in Bayesian Confirmatory Factor Analysis (BCFA). In standard PPMC procedures, model misfit is quantified by comparing the location of an ML-based point estimate to the predictive distribution of a statistic. When the point estimate is far from the center posterior predictive distribution, model fit is poor. Not included in this approach, however, is the variability of the Maximum Likelihood (ML)-based point estimates. We propose a new method of PPMC based on comparing posterior predictive distributions of a hypothesized and saturated BCFA model.

Diagnostic classification models (DCMs) are restricted latent class models with a set of cross-class equality constraints and additional monotonicity constraints on their item parameters, both of which are needed to ensure the meaning of classes and model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs with monotonicity constraints.

The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL.

Examining teachers’ knowledge on a large scale involves addressing substantial measurement and logistical issues; thus, existing teacher knowledge assessments have mainly consisted of selected-response items because of their ease of scoring. Although open-ended responses could capture a more complex understanding of and provide further insights into teachers’ thinking, scoring these responses is expensive and time consuming, which limits their use in large-scale studies. In this study, we investigated whether a novel statistical approach, topic modeling, could be used to score teachers’ open-ended responses and if so, whether these scores would capture nuances of teachers’ understanding.

In this work, we extend variational auto encoders (VAE) to estimate item parameters and correlated latent abilities, and directly compare the ML2P-VAE method to more traditional parameter estimation methods, such as Monte Carlo expectation-maximization. The incorporation of a non-identity covariance matrix in a VAE requires a novel VAE architecture, which can be utilized in applications outside of education.

Diagnostic classification models (DCMs) are psychometric models for evaluating a student’s mastery of the essential skills in a content domain based upon their responses to a set of test items. Currently, diagnostic model and/or Q-matrix misspecification is a known problem with limited avenues for remediation. To address this problem, this paper defines a one-sided score statistic that is a computationally efficient method for detecting under-specification at the item level of both the Q-matrix and the model parameters of the particular DCM chosen in an analysis.

This book is about scientific inquiry. Designed for early and mid-career researchers, it is a practical manual for conducting and communicating high-quality research in (mathematics) education. Based on the authors’ extensive experience as researchers, as mentors, and as members of the editorial team for the Journal for Research in Mathematics Education (JRME), this book directly speaks to researchers and their communities about each phase of the process for conceptualizing, conducting, and communicating high-quality research in (mathematics) education.

As distinct communities of practice (COP), science education research (SER) and environmental education research (EER) have both matured a great deal in recent decades, coming to include a greater diversity of theoretical perspectives, worldviews, and researcher and participant voices. In this paper, we present a view of theoretical inclusivity that promises a rich, robust research landscape for both EER and SER through the deliberate inclusion of non-Western theories.

This study investigates the emergence and cultivation of teachers' “epistemic empathy” in response to analyzing videos of student inquiry. We define epistemic empathy as the act of understanding and appreciating someone's cognitive and emotional experience within an epistemic activity—i.e., activity aimed at the construction, communication, and critique of knowledge. Our goals are (1) to conceptually develop the construct and contrast it to more general notions of caring and (2) to empirically examine epistemic empathy in the context of preservice teacher education. We discuss tensions in teachers' expressions of epistemic empathy, and we end with implications for research and practice.