Performances of Collapsed Gibbs Sampling, Posterior Mode Estimation and Joint Maximum Likelihood Estimation on Diagnostic Classification Models for Boundary Problems

Jingyang Li, Zhenqiu Lu, Matthew Madison, Zuchao Shen

DOI: 10.64028/rqjc519600

Keywords: diagnostic classification models, collapsed Gibbs sampling, posterior mode estimation, joint maximum likelihood estimation, boundary problem, Bayesian estimation

Abstract: Diagnostic Classification Models (DCMs) assess latent cognitive attributes but often suffer from boundary problems, where slipping and guessing parameters converge to 0 or 1, reducing classification accuracy. This study compares Collapsed Gibbs Sampling (CGS), Posterior Mode Estimation (PME), and Joint Maximum Likelihood Estimation (JMLE) in addressing this issue via Monte Carlo simulation. By varying sample size, item quality, dimensionality, and test length, we examine classification accuracy and boundary problem rates. Results show CGS and JMLE generally yield higher accuracy, while PME consistently maintains the lowest boundary problem occurrence rate. PME is generally computationally efficient in simpler settings, CGS offers stable performance, and JMLE can be competitive under specific conditions.

Submission Number: 25