Latent Space Model for Process Data

Abstract

The development of human-computer interactive items in educational assessments provides opportunities to extract useful process information for problem-solving. However, the complex, intensive, and noisy nature of process data makes it challenging to model with the traditional psychometric methods. Social network methods have been applied to visualize and analyze process data. Nonetheless, research about statistical modeling of process information using social network methods is still limited. This article explored the application of the latent space model (LSM) for analyzing process data in educational assessment. The adjacent matrix of transitions between actions was created based on the weighted and directed network of action sequences and related auxiliary information. Then, the adjacent matrix was modeled with LSM to identify the lower-dimensional latent positions of actions. Three applications based on the results from LSM were introduced: action clustering, error analysis, and performance measurement. The simulation study showed that LSM can cluster actions from the same problem-solving strategy and measure students’ performance by comparing their action sequences with the optimal strategy. Finally, we analyzed the empirical data from PISA 2012 as a real case scenario to illustrate how to use LSM.