Multidimensional Item Response Theory in the Style of Collaborative Filtering

Area of Science:

• Educational Measurement
• Machine Learning
• Psychometrics

Background:

• Multidimensional item response theory (MIRT) models latent traits from assessment data.
• Traditional MIRT analysis faces challenges with large, sparse datasets and factor interpretation.

Purpose of the Study:

• To develop a machine learning framework for MIRT.
• To enable efficient analysis of large-scale, sparse assessment data.
• To propose alternative validation methods for high-dimensional MIRT models.

Main Methods:

• A general class of MIRT models inspired by collaborative filtering.
• Penalized joint maximum likelihood for model estimation.
• Cross-validation for model selection and batching for efficiency.

Main Results:

• The proposed machine learning approach effectively models and predicts student performance.
• Efficient analysis of large and sparse datasets is demonstrated with simulated and real-world data.
• An alternative validation method using item popularity is proposed for complex factor models.

Conclusions:

• Machine learning offers a powerful approach to MIRT, enhancing scalability and efficiency.
• The method provides a viable alternative for analyzing complex, high-dimensional assessment data.
• Novel validation strategies are crucial for interpreting results from large-scale MIRT applications.