A latent topic model with Markov transition for process data |
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Authors: | Haochen Xu Guanhua Fang Zhiliang Ying |
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Institution: | 1. Fudan University, Shanghai, China;2. Columbia University, New York, New York, USA |
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Abstract: | We propose a latent topic model with a Markov transition for process data, which consists 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 the 2012 version of the Programme for International Student Assessment (PISA). |
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Keywords: | process data hierarchical Bayesian hidden Markov model variational EM PISA 2012 |
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