Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and…

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables…

Model evaluation -- the process of making inferences about the performance of predictive models -- is a critical component of predictive modelling research in learning analytics. We survey the state of the practice with respect to model evaluation in learning analytics, which overwhelmingly uses only naïve methods for model evaluation or…

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…

When a new student comes to play an educational game, how can we determine what content to give them such that they learn as much as possible? When a frustrated customer calls in to a helpline, how can we determine what to say to best assist them? When an ill patient comes in to the clinic, how do we determine what tests to run and treatments to…

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

Personalization, the idea that teaching can be tailored to each students' needs, has been a goal for the educational enterprise for at least 2,500 years (Regian, Shute, & Shute, 2013, p.2). Recently personalization has picked up speed with the advent of mobile computing, the Internet and increases in computer processing power. These changes…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

A long-standing challenge for knowledge tracing is how to update estimates of multiple subskills that underlie a single observable step. We characterize approaches to this problem by how they model knowledge tracing, fit its parameters, predict performance, and update subskill estimates. Previous methods allocated blame or credit among subskills…

Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive,…

In their influential "Psychological Review" article, Bogacz, Brown, Moehlis, Holmes, and Cohen (2006) discussed optimal decision making as accomplished by the drift diffusion model (DDM). The authors showed that neural inhibition models, such as the leaky competing accumulator model (LCA) and the feedforward inhibition model (FFI), can mimic the…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

An application of a hierarchical IRT model for items in families generated through the application of different combinations of design rules is discussed. Within the families, the items are assumed to differ only in surface features. The parameters of the model are estimated in a Bayesian framework, using a data-augmented Gibbs sampler. An obvious…

"Growth mixture models" (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class…