Bayesian Inference for Unknown Number of Attributes in Cognitive Diagnosis Models

• In Event: Advancing Diagnostic Psychometric Models to Enhance Student Learning: Statistical Theory, Methods, and Applications

Abstract

The specification of the Q matrix in cognitive diagnosis models is important for correct classification of attribute profiles. Researchers have proposed many methods for estimation and validation of the data-driven Q matrices. However, inference of the number of attributes in the general restricted latent class model remains an open question. We propose a Bayesian framework for general restricted latent class models and use the spike-and-slab prior to avoid the computation issues caused by the varying dimensions of model parameters associated with the number of attributes, K. We develop an efficient Metropolis-within-Gibbs algorithm to estimate K and the corresponding Q matrix simultaneously. The proposed algorithm uses the stick-breaking construction to mimic an Indian buffet process and employs a novel Metropolis-Hastings transition step to encourage exploring the sample space associated with different values of K. We evaluate the performance of the proposed method through a simulation study under different model specifications and apply the method to a real data set related to a fluid intelligence matrix reasoning test.

Authors

• Yinghan Chen, University of Nevada - Reno
  Presenting Author

• Steven Andrew Culpepper, University of Illinois at Urbana-Champaign
  Non-Presenting Author