Abstract:
Cognitive diagnostic models (CDMs) provide a framework for assessing individuals’ mastery of specific skills or attributes. Traditional CDMs represent mastery through discrete attribute profiles, which may be overly restrictive when underlying skills vary continuously. Partial-mastery CDMs (PM-CDMs) accommodate continuous levels of attribute mastery while retaining the diagnostic structure of traditional CDMs.
In this talk, I investigate the identifiability and estimation of parametric PM-CDMs. I first discuss their connections to item response theory models and investigate conditions for local identifiability. I then compare data-augmented Gibbs sampling and stochastic approximation algorithm across models with conjunctive, additive, and interaction-based response functions. Simulation studies evaluate their finite-sample performance and reveal challenges in jointly estimating item parameters and latent attribute distributions. Finally, an application to data from the Examination for the Certificate of Proficiency in English (ECPE) illustrates how different item response structures influence model fit.
Jun Wu is a postdoctoral fellow in the Computational Psychometrics Group, Czech Academy of Sciences. His research interests are in graphical models and latent variable models.
