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This study presents a comprehensive analysis of three types of multimodal data‐response accuracy, response times, and eye‐tracking data‐derived from a computer‐based spatial rotation test. To tackle the complexity of high‐dimensional data analysis challenges, we have developed a methodological framework incorporating various statistical and machine learning methods. The results of our study reveal that hidden state transition probabilities, based on eye‐tracking features, may be contingent on skill mastery estimated from the fluency CDM model. The hidden state trajectory offers additional diagnostic insights into spatial rotation problem‐solving, surpassing the information provided by the fluency CDM alone. Furthermore, the distribution of participants across different hidden states reflects the intricate nature of visualizing objects in each item, adding a nuanced dimension to the characterization of item features. This complements the information obtained from item parameters in the fluency CDM model, which relies on response accuracy and response time. Our findings have the potential to pave the way for the development of new psychometric and statistical models capable of seamlessly integrating various types of multimodal data. This integrated approach promises more meaningful and interpretable results, with implications for advancing the understanding of cognitive processes involved in spatial rotation tests. 

Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a Bayesian formulation for attribute hierarchy within CDM framework and developed an efficient Metropolis within Gibbs algorithm to estimate the underlying hierarchy along with the specified CDM parameters. Our proposed estimation method is flexible and can be adapted to a general class of CDMs. We demonstrated our proposed method via a simulation study, and the results from which show that the proposed method can fully recover or estimate at least a subgraph of the underlying structure across various conditions under a specified CDM model. The real data application indicates the potential of learning attribute structure from data using our algorithm and validating the existing attribute hierarchy specified by content experts. 

Advances in educational technology provide teachers and schools with a wealth of information about student performance. A critical direction for educational research is to harvest the available longitudinal data to provide teachers with real-time diagnoses about students’ skill mastery. Cognitive diagnosis models (CDMs) offer educational researchers, policy makers, and practitioners a psychometric framework for designing instructionally relevant assessments and diagnoses about students’ skill profiles. In this article, the authors contribute to the literature on the development of longitudinal CDMs, by proposing a multivariate latent growth curve model to describe student learning trajectories over time. The model offers several advantages. First, the learning trajectory space is high-dimensional and previously developed models may not be applicable to educational studies that have a modest sample size. In contrast, the method offers a lower dimensional approximation and is more applicable for typical educational studies. Second, practitioners and researchers are interested in identifying factors that cause or relate to student skill acquisition. The framework can easily incorporate covariates to assess theoretical questions about factors that promote learning. The authors demonstrate the utility of their approach with an application to a pre- or post-test educational intervention study and show how the longitudinal CDM framework can provide fine-grained assessment of experimental effects.