Sequential Gibbs Sampling Algorithm for Cognitive Diagnosis Models with Many Attributes

TL;DR

This paper introduces a sequential Gibbs sampling algorithm for cognitive diagnosis models that significantly reduces computational complexity from exponential to linear in the number of attributes, enabling efficient inference with many attributes.

Contribution

The paper proposes a novel sequential Gibbs sampling method that improves computational efficiency for high-dimensional cognitive diagnosis models.

Findings

The method demonstrates good finite-sample performance in simulations.

It outperforms existing MCMC algorithms in computational speed.

Real data examples confirm its practical advantages.

Abstract

Cognitive diagnosis models (CDMs) are useful statistical tools to provide rich information relevant for intervention and learning. As a popular approach to estimate and make inference of CDMs, the Markov chain Monte Carlo (MCMC) algorithm is widely used in practice. However, when the number of attributes, $K$, is large, the existing MCMC algorithm may become time-consuming, due to the fact that $O(2^K)$ calculations are usually needed in the process of MCMC sampling to get the conditional distribution for each attribute profile. To overcome this computational issue, motivated by Culpepper and Hudson (2018), we propose a computationally efficient sequential Gibbs sampling method, which needs $O(K)$ calculations to sample each attribute profile. We use simulation and real data examples to show the good finite-sample performance of the proposed sequential Gibbs sampling, and its advantage over existing methods.