A Latent Topic Model with Markovian Transition for Process Data

Haochen Xu; Guanhua Fang; Zhiliang Ying

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arXiv · 1911.01583

A Latent Topic Model with Markovian Transition for Process Data

Haochen Xu·Guanhua Fang·Zhiliang Ying

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Abstract

We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem solving item in 2012 Programme for International Student Assessment (PISA 2012).

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Haochen Xu, Guanhua Fang, Zhiliang Ying. 2019-11-05. A Latent Topic Model with Markovian Transition for Process Data. https://arxiv.org/abs/1911.01583

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