A latent topic model with Markov transition for process data.

Area of Science:

• Educational Measurement
• Machine Learning
• Data Mining

Background:

• Process data, comprising time-stamped events, is increasingly prevalent in computer-based educational assessments, particularly for complex problem-solving items.
• Understanding examinee states and learning trajectories is crucial for effective assessment and feedback.

Purpose of the Study:

• To propose a novel latent topic model incorporating Markov transitions for analyzing process data in educational assessments.
• To extend hierarchical Bayesian topic models with hidden Markov structures to capture evolving examinee latent states.

Main Methods:

• Development of a latent topic model with Markov transitions for time-stamped event data.
• Utilizing topic transition probabilities and response times to model examinee learning trajectories.
• Implementation of a forward-backward variational expectation-maximization (FB-VEM) algorithm for computational efficiency.

Main Results:

• The model effectively captures examinees' learning trajectories by integrating topic transition probabilities and response times.
• The FB-VEM algorithm provides an efficient method for tackling the computational challenges of the proposed model.
• Theoretical properties of the model are established under specific asymptotic conditions.

Conclusions:

• The proposed latent topic model with Markov transitions offers a powerful tool for analyzing complex problem-solving processes in educational assessments.
• This approach enhances the efficiency of examinee clustering and classification by modeling learning trajectories.
• The method was successfully applied to a complex problem-solving item from the 2012 Programme for International Student Assessment (PISA).