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).

中文翻译：

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具有马尔可夫转换的过程数据的潜在主题模型

我们为过程数据提出了一个带有马尔可夫转换的潜在主题模型，它由记录在日志文件中的时间戳事件组成。此类数据在具有复杂问题解决项目的基于计算机的教育评估中变得越来越广泛。所提出的模型可以被视为分层贝叶斯主题模型的扩展，具有隐藏的马尔可夫结构，以适应考生潜在状态的潜在演变。使用主题转移概率和响应时间使我们能够捕捉考生的学习轨迹，使聚类/分类更有效。开发了一种前向-后向变分期望最大化（FB-VEM）算法来解决具有挑战性的计算问题。在某些渐近机制下建立了有用的理论性质。