Maximum Marginal Likelihood Estimation With an Expectation–Maximization Algorithm for Multigroup/Mixture Multidimensional Item Response Theory Models

Marginal Maximum Likelihood Estimation of Item Response Models in R

Item response theory (IRT) models are a class of statistical models used by researchers to describe the response behaviors of individuals to a set of categorically scored items. The most common IRT models can be classified as generalized linear fixedand/or mixed-effect models. Although IRT models appear most often in the psychological testing literature, researchers in other fields have success...

A New Algorithm for Maximum Likelihood Estimation in Gaussian Graphical Models for Marginal Independence

Graphical models with bi-directed edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorith...

A New Algorithm for Maximum Likelihood Estimation in GaussianGraphi al Models for Marginal Independen e

Likelihood and Fairness in Multidimensional Item Response Theory

In multidimensional item response theory, it is possible for the estimate of a subject’s ability in some dimension to decrease after they have answered a question correctly. When this occurs, the fairness of the estimate may be called into question. This paper investigates how and when this form of non-monotonicity occurs. We demonstrate that many response models and statistical estimates can p...

Parameter Estimation with Mixture Item Response Theory Models: A Monte Carlo Comparison of Maximum Likelihood and Bayesian Methods