An Efficient Variational Bayes Algorithm via Pólya–Gamma Data Augmentation Technique for Estimating the DINA Model

Abstract

Cognitive diagnostic models (CDMs) are widely applied in educational and psychological measurement, and variational Bayes (VB) algorithms have recently gained attention for parameter estimation. In this paper, we propose a novel VB-based algorithm, termed Variational Bayes via Pólya-Gamma (VB-PG), which leverages the Pólya–Gamma data augmentation technique. The method is developed for the reparameterized deterministic inputs, noisy “and” gate (DINA) model, providing an efficient and accurate framework for parameter estimation. By introducing Pólya–Gamma data augmentation method, VB-PG algorithm achieves a streamlined implementation with fully closed-form updates for all unknown variables. Simulation studies show that the VB-PG algorithm outperforms both existing VB methods, the expectation-maximization (EM) algorithm, and the Markov chain Monte Carlo (MCMC) algorithm, yielding higher estimation accuracy, particularly for slope parameters under small samples, and superior computational efficiency. An empirical example analysis further confirms its robustness and practical advantages, demonstrating that the VB-PG algorithm provides a simpler, faster, and more accurate solution for parameter estimation in the DINA model.

Keywords

cognitive diagnostic models variational Bayes Pólya-Gamma DINA model

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