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As a statistical tool to assist formative assessments in educationalsettings, diagnostic classification models (DCMs) have been increasingly usedto provide diagnostic information regarding examinees' attributes. DCMs oftenadopt a dichotomous division such as the mastery and non-mastery of attributesto express the mastery states of attributes. However, many practical settingsinvolve different levels of mastery states rather than a simple dichotomy in asingle attribute. Although this practical demand can be addressed bypolytomous-attribute DCMs, their computational cost in a Markov chain MonteCarlo estimation impedes their large-scale application due to the larger numberof polytomous-attribute mastery patterns than that of binary-attribute ones.This study considers a scalable Bayesian estimation method forpolytomous-attribute DCMs and developed a variational Bayesian (VB) algorithmfor a polytomous-attribute saturated DCM -- a generalization ofpolytomous-attribute DCMs -- by building on the existing literature onpolytomous-attribute DCMs and VB for binary-attribute DCMs. Furthermore, weproposed the configuration of parallel computing for the proposed VB algorithmto achieve better computational efficiency. Monte Carlo simulations revealedthat our method exhibited the high performance in parameter recovery under awide range of conditions. An empirical example is used to demonstrate theutility of our method.

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