Estimating LLM Grading Ability and Response Difficulty in Automatic Short Answer Grading via Item Response Theory
Authors: Longwei Cong, Sonja Hahn, Sebastian Gombert, Leon Camus, Hendrik Drachsler, Ulf Kroehne
Organizations: DIPF | Leibniz Institute for Research and Information in Education · Faculty of Computer Science, Goethe University Frankfurt · 3Chemnitz University of Technology
Automated short answer grading (ASAG) with large language models (LLMs) is commonly evaluated with aggregate metrics such as macro-F1 and Cohen's kappa. However, these metrics provide limited insight into how grading performance varies across student responses of differing grading difficulty. We introduce an evaluation framework for LLM-based ASAG based on item response theory (IRT), which models grading correctness as a function of latent grader ability and response grading difficulty. This formulation enables response-level analysis of where LLM graders succeed or fail and reveals robustness differences that are not visible from aggregate scores alone. We apply the framework to 17 open-weight LLMs on the SciEntsBank and Beetle benchmarks. The results show that even models with similar overall performance differ substantially in how sharply their grading accuracy declines as response difficulty increases. In addition, confusion patterns show that errors on difficult responses concentrate disproportionately on the \texttt{partially_correct_incomplete} label, indicating a tendency toward intermediate-label collapse under ambiguity. To characterize difficult responses, we further analyze semantic and linguistic correlates of estimated difficulty. Across both datasets, higher difficulty is associated with weaker semantic alignment to the reference answer, stronger contradiction signals, and greater semantic isolation in embedding space. Overall, these results show that item response theory offers a useful framework for evaluating LLM-based ASAG beyond aggregate performance measures.
Automatic Short Answer Grading (ASAG) with generative large language models (LLMs) has recently demonstrated strong performance without task-specific fine-tuning, while also enabling the generation of synthetic feedback for educational assessment. Despite these advances, LLM-based grading remains imperfect, making reliable confidence estimates essential for safe and effective human-AI collaboration in educational decision-making. In this work, we investigate confidence estimation for ASAG with LLMs by jointly considering model-based confidence signals and dataset-derived uncertainty. We systematically compare three model-based confidence estimation strategies, namely verbalizing, latent, and consistency-based confidence estimation, and show that model-based confidence alone is insufficient to reliably capture uncertainty in ASAG. To address this limitation, we propose a hybrid confidence framework that integrates model-based confidence signals with an explicit estimate of dataset-derived aleatoric uncertainty. Aleatoric uncertainty is operationalized by clustering semantically embedded student responses and quantifying within-cluster heterogeneity. Our results demonstrate that the proposed hybrid confidence measure yields more reliable confidence estimates and improves selective grading performance compared to single-source approaches. Overall, this work advances confidence-aware LLM-based grading for human-in-the-loop assessment, supporting more trustworthy AI-assisted educational assessment systems.
Automated short answer scoring (ASAS) is shifting from discriminative, fine-tuned models to large language models (LLMs) used in few-shot settings. This paradigm leverages LLMs broad world knowledge and ease of deployment, but limited task-specific data may reduce alignment on complex scoring tasks. In particular, its impact on scoring partially correct responses that require nuanced interpretation remains underexplored. We investigate the relationship between the degree of task-specific adaptation of different models and quality-conditioned scoring agreement. We compare three LLMs (GPT-5.2, GPT-4o, Claude Opus 4.5) in few-shot mode, a fine-tuned BERT-based encoder, and a human expert on two open-ended biology items, using several hundred student responses and ground truth scores provided by a biology education expert. The results show that human-human agreement is highest and stable across the full quality spectrum. All AI models perform well on fully correct and fully incorrect responses, but exhibit substantial degradation on mid-range responses. This mid-range degradation is conditioned on task-specific adaptation: It is most severe in few-shot LLMs with few examples and decreases as task-specific data increases, with fine-tuned encoder models performing best. This mid-range degradation may lead to inequitable evaluation of responses produced by students with developing understanding. Our findings highlight the importance of quality-conditioned fairness, with particular attention to mid-range responses.
Abigail Victoria Gurin Schleifer, Moriah Ariely, Beata Beigman Klebanov +2
Item discrimination is a fundamental psychometric property of educational assessment, which measures whether an item meaningfully distinguishes students with higher proficiency from students with lower proficiency. While various existing works have explored whether large language models (LLMs) can estimate item difficulty, it remains unclear whether they can capture item discrimination. In this work, we evaluate 42 proprietary and open-weight LLMs in zero-shot settings using two complementary approaches: direct discrimination prediction, where models explicitly estimate an item's discrimination value from its content, and response-based Classical Test Theory (CTT) calibration, where LLM answers are treated as synthetic student responses to compute discrimination scores. Our results show that direct prediction yields weak alignment with human-calibrated discrimination: the best-performing model reaches only a Spearman correlation of 0.152. Response-based CTT calibration provides a stronger but still limited signal, with the all-persona synthetic respondent pool reaching a Spearman correlation of 0.241. These findings highlight item discrimination as an open challenge for LLM-based psychometric evaluation: current LLMs contain non-random discrimination-relevant signal, but they do not yet reliably capture how assessment items distinguish human students.