Hierarchical Bayesian Multi-Dimensional IRT Applied to 200k Concept Tests
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mathematics-14-02398-v2.pdf
Size
1.53 MB
Format
Adobe PDF
Checksum (MD5)
d09b01b7b6e5846229a38de315c829c1
Author(s)
Segado, Martin
Adair, Aaron
Dange, Atharva
Deng, Miaoyi
Pritchard, David
Date Issued
July 4, 2026
Journal
Mathematics
Publisher
MDPI
Citation
Segado, M.; Adair, A.; Dange, A.; Deng, M.; Pritchard, D. Hierarchical Bayesian Multi-Dimensional IRT Applied to 200k Concept Tests. Mathematics 2026, 14, 2398.
Version
Final published version
Abstract
We report the use of our group’s hierarchical Bayesian implementation of the multi-dimensional nominal categories model followed by standard factor rotations of the principal dimensions to obtain 28 curated sparse dimensions from a set of 203,564 (104,998 pre- and 98,566 post-) administrations of a multiple-choice concept test in mechanics. We emphasize our careful attention to issues common to fitting such multi-parameter models to large datasets: a novel set of filters to remove administrations of questionable validity, the use of Bayesian methods to avoid overfitting, selecting the best transformations to find easily identifiable sparse dimensions, and verification and pruning of these using bootstrap samples. We demonstrate that these dimensions are invariant across demographically different samples of students as well as between pre-instruction and post-instruction samples. Most sparse dimensions correspond to well-known misconceptions in mechanics.
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/math14132398
