Count responses with grouping and right censoring have long been used in surveys to study a variety of behaviors, status, and attitudes. Yet grouping or right-censoring decisions of count responses still rely on arbitrary choices made by researchers. We develop a new method for evaluating grouping and right-censoring decisions of count responses…

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…

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…

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…

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…

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,…

For any density function (or probability function), there always corresponds a "cumulative distribution function" (cdf). It is a well-known mathematical fact that the cdf is more general than the density function, in the sense that for a given distribution the former may exist without the existence of the latter. Nevertheless, while the…

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…

Association models constitute an attractive alternative to the usual log-linear models for modeling the dependence between classification variables. They impose special structure on the underlying association by assigning scores on the levels of each classification variable, which can be fixed or parametric. Under the general row-column (RC)…

Student modeling is a widely used approach to make inference about a student's attributes like knowledge, learning, etc. If we wish to use these models to analyze and better understand student learning there are two problems. First, a model's ability to predict student performance is at best weakly related to the accuracy of any one of its…

This paper provides a history of ETS's role in developing assessment instruments and psychometric procedures for measuring change in large-scale national assessments funded by the Longitudinal Studies branch of the National Center for Education Statistics. It documents the innovations developed during more than 30 years of working with…

Anomaly detection is an important and indispensable aspect of any computer security mechanism. Ad hoc and mobile networks consist of a number of peer mobile nodes that are capable of communicating with each other absent a fixed infrastructure. Arbitrary node movements and lack of centralized control make them vulnerable to a wide variety of…