Large language models (LLMs) are widely used as automatic judges, with validity typically assessed via alignment with human scores. However, aggregate agreement fails to reveal whether humans and LLMs find the same evaluation cases difficult. In this paper, we study this problem in summarization evaluation from a psychometric perspective. We fit Many-Facet Rasch Models separately to human and LLM ratings to decompose scores into latent summary quality, rater severity, dimension severity, and rating-scale thresholds. Building on this decomposition, we define residual hardness as a model-adjusted measure of judging difficulty and compare whether human and LLM judges share the same hardness structure.

Across 17 open-weight LLM judges on SummEval, we find that moderate alignment in latent summary quality does not imply alignment in residual hardness. Human and LLM judges differ in which summary–dimension units remain difficult, and this mismatch is strongly dimension-dependent. Consistency shows a pronounced LLM-hard shift, whereas coherence shows a human-hard shift. We further show that human-easy but LLM-hard cases are partially predictable from observable source–summary properties. These findings suggest that aggregate human alignment reflects only part of LLM-as-judge reliability, while psychometric residual diagnostics support more informative judge evaluation and more targeted human–LLM collaboration.

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 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.