Estimating Bayesian Diagnostic Models with Attribute Hierarchies with the Hamiltonian-Gibbs Hybrid Sampler

Abstract

In this study, we propose a synthesis of HMC with the Gibbs sampler for estimating Bayesian diagnostic classification models. The Gibbs sampler is well-suited for sampling categorical parameters as only the full conditional distribution of the attributes is needed and can be obtained in closed form. Our approach—the Hamiltonian-Gibbs (HG) hybrid sampler partitions the parameter space into continuous and discrete parameter blocks and utilizes HMC to update continuous parameters (i.e., item parameters) and Gibbs sampling to update discrete parameters (i.e., attributes).

Alfonso J. Martinez

Assistant Professor of Psychometrics and Quantitative Psychology

My research interests include generalized latent variable modeling, Bayesian analysis, and computational statistics.