A family of learning models that integrates a cognitive diagnostic model and a higher-order, hidden Markov model in one framework is proposed. This new framework includes covariates to model skill transition in the learning environment. A Bayesian formulation is adopted to estimate parameters from a learning model. The developed methods are…

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993)and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT…