Variational Bayesian Inference for a Polytomous-Attribute Saturated Diagnostic Classification Model with Parallel Computing

TL;DR

This paper introduces a scalable variational Bayesian estimation method for polytomous-attribute diagnostic classification models, significantly improving computational efficiency for large-scale educational assessment data.

Contribution

It develops a novel variational Bayesian algorithm for a generalized polytomous-attribute DCM and incorporates parallel computing to enhance scalability.

Findings

High accuracy in parameter recovery across various conditions

Efficient computation with parallelized VB algorithm

Effective application demonstrated through empirical example

Abstract

As a statistical tool to assist formative assessments in educational settings, diagnostic classification models (DCMs) have been increasingly used to provide diagnostic information regarding examinees' attributes. DCMs often adopt a dichotomous division such as the mastery and non-mastery of attributes to express the mastery states of attributes. However, many practical settings involve different levels of mastery states rather than a simple dichotomy in a single attribute. Although this practical demand can be addressed by polytomous-attribute DCMs, their computational cost in a Markov chain Monte Carlo estimation impedes their large-scale application due to the larger number of polytomous-attribute mastery patterns than that of binary-attribute ones. This study considers a scalable Bayesian estimation method for polytomous-attribute DCMs and developed a variational Bayesian (VB) algorithm for a polytomous-attribute saturated DCM -- a generalization of polytomous-attribute DCMs -- by building on the existing literature on polytomous-attribute DCMs and VB for binary-attribute DCMs. Furthermore, we proposed the configuration of parallel computing for the proposed VB algorithm to achieve better computational efficiency. Monte Carlo simulations revealed that our method exhibited the high performance in parameter recovery under a wide range of conditions. An empirical example is used to demonstrate the utility of our method.