Student modeling is one of the most important processes in adaptive systems. Although learning is individual, a model can be created based on patterns in student behavior. Since a student model can be created for more than one student, the use of machine learning techniques in student modeling is increasing. Artificial neural networks (ANNs),…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis…

The present article considers a fundamental question in evaluation research: "By how much do program effects vary across sites?" The article first presents a theoretical model of cross-site impact variation and a related estimation model with a random treatment coefficient and fixed site-specific intercepts. This approach eliminates…

Information changes as it is passed from person to person, with this process of cultural transmission allowing the minds of individuals to shape the information that they transmit. We present mathematical models of cultural transmission which predict that the amount of information passed from person to person should affect the rate at which that…

In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

In educational technology and learning sciences, there are multiple uses for a predictive model of whether a student will perform a task correctly or not. For example, an intelligent tutoring system may use such a model to estimate whether or not a student has mastered a skill. We analyze the significance of data recency in making such…

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

The purpose of this study was to explore the degree of grain size of the attributes and the sample sizes that can support accurate parameter recovery with the General Diagnostic Model (GDM) for a large-scale international assessment. In this resampling study, bootstrap samples were obtained from the 2003 Grade 8 TIMSS in Mathematics at varying…

Studied the order-statistics models, extending the usual normal order-statistics model into one in which the underlying random variables followed a multivariate normal distribution. Used a Bayesian approach and the Gibbs sampling technique. Applied the proposed method to analyze presidential election data from the American Psychological…

Discusses , in the context of confirmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Uses a small simulation study to show that in this context, Bayes factors and the pseudo likelihood ratio statistics have the best properties. (SLD)

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variable as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The proposed estimation methods are illustrated by two simulation studies. (SLD)

A Bayesian approach to the testing of competing covariance structures is developed. Approximate posterior probabilities are easily obtained from the chi square values and other known constants. The approach is illustrated using an example that demonstrates how the prior probabilities can alter results concerning the preferred model specification.…

The Akaike Information Criterion (AIC) was introduced to extend the method of maximum likelihood to the multimodel situation. Use of the AIC in factor analysis is interesting when it is viewed as the choice of a Bayesian model; thus, wider applications of AIC are possible. (Author/GDC)