This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

Given the necessity to bridge the gap between what happened and what is likely to happen, this paper aims to explore how to apply Bayesian inference to cost-effectiveness analysis so as to capture the uncertainty of a ratio-type efficiency measure. The first part of the paper summarizes the characteristics of the evaluation data that are commonly…

Memories for spatial locations often show systematic errors toward the central value of the surrounding region. The Category Adjustment (CA) model suggests that this bias is due to a Bayesian combination of categorical and metric information, which offers an optimal solution under conditions of uncertainty (Huttenlocher, Hedges, & Duncan,…

A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

The Vanishing Tetrad Test (VTT) (Bollen, Lennox, & Dahly, 2009; Bollen & Ting, 2000; Hipp, Bauer, & Bollen, 2005) is an extension of the Confirmatory Tetrad Analysis (CTA) proposed by Bollen and Ting (Bollen & Ting, 1993). VTT is a powerful tool for detecting model misspecification and can be particularly useful in cases in which…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

When combining results across related studies, a multivariate meta-analysis allows the joint synthesis of correlated effect estimates from multiple outcomes. Joint synthesis can improve efficiency over separate univariate syntheses, may reduce selective outcome reporting biases, and enables joint inferences across the outcomes. A common issue is…

The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance…

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

We report an experiment designed to provide a qualitative contrast between knowledge-limited versions of mixed-state and variable-resources (VR) models of visual change detection. The key data pattern is that observers often respond "same" on big-change trials, while simultaneously being able to discriminate between same and small-change…

Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular because of their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (although richer than standard meta-analysis, comparing only two…

While Educational Data Mining research has traditionally emphasized the practical aspects of learner modeling, such as predictive modeling, estimating students knowledge, and informing adaptive instruction, in the current study, we argue that Educational Data Mining can also be used to test and improve our fundamental theories of human learning.…

Diagnostic models combine multiple binary latent variables in an attempt to produce a latent structure that provides more information about test takers' performance than do unidimensional latent variable models. Recent developments in diagnostic modeling emphasize the possibility that multiple skills may interact in a conjunctive way within the…

Bayesian Knowledge Tracing (BKT) has been in wide use for modeling student skill acquisition in Intelligent Tutoring Systems (ITS). BKT tracks and updates student's latent mastery of a skill as a probability distribution of a binary variable. BKT does so by accounting for observed student successes in applying the skill correctly, where success is…