Response-free item difficulty modelling for multiple-choice items with fine-tuned transformers: Component-wise representation and multi-task learning
Authors: Jan Netík, Patrícia Martinková
Organizations: Faculty of Education, Charles University, Prague, Czech Republic · Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic
Abstract
Item difficulty must often be estimated before test administration, when no responses are yet available for calibration. While most response-free difficulty modelling approaches derive item-text features by hand for a separate statistical model, we fine-tune a transformer end-to-end on the wording, avoiding the theory-based feature design and the preprocessing that discards information. We address reading-comprehension multiple-choice items, whose difficulty depends on inferential demands spanning passage, question, and options, yet the simplest model sees one undifferentiated sequence and is trained on difficulty alone. We introduce and investigate two extensions to the joint-encoding baseline: a component-wise variant, which encodes the wording parts separately, and a multi-task variant, which adds an auxiliary task of question answering. We compare the methods across three training-set sizes sampled from a corpus of nearly 30,000 items whose labels approximate response-based Rasch difficulty. At the smallest training size, both extensions improve on the baseline, the multi-task variant across every metric, and component-wise encoding in rank ordering. Further research may ground the auxiliary supervision in observed responses and extend the approach to other item types.
We present results from reconstructing multiple-choice model (MCM) and three-parameter logistic (3PL) model curves using a fine-tuned multimodal large language model (LLM) based on Qwen3.5. The model is prompted and fine-tuned to replicate choice probabilities across a large training corpus of multiple-choice items containing both image and text stimuli, conditioned on a labeled set of student ability levels. By learning to reproduce the systematic error patterns of students across a discrete range of abilities, the LLM implicitly captures the underlying response probabilities encoded in the 3PL and MCM curves. This allows us to accurately approximate item difficulty on a held-out test set directly from the model's predicted option probabilities.
Most multiple-choice question (MCQ) benchmarks evaluate Large Language Models (LLMs) only by whether they select the correct answers. This binary scoring treats all incorrect responses alike, even though an LLM's preferences among incorrect options may contain systematic and useful information about its behavior and ability. We introduce the LLM Nominal Response Model (LLM-NRM), an option-aware psychometric framework that models the full distribution over answer choices to jointly estimate LLM ability and option-level item characteristics, while separating model-specific response calibration sharpness, positional preference, and difficulty-dependent fallback behavior. Across 189 LLMs and 31,554 items from 14 benchmarks, LLM-NRM predicts held-out LLM-item interactions more accurately than binary Item Response models and conventional nominal-response baselines, and its ability estimates achieve the strongest Spearman correlation of 0.920 with the external human-preference Arena.ai Elo leaderboard. Distractor identity contributes +101% additional Fisher Information per item beyond correctness, and incorrect responses alone recover full-information ability estimates with Spearman 0.943. The learned item parameters also enable efficient benchmarking, where 41 selected items preserve the full-bank ranking with Kendall's correlation 0.85, corresponding to a 770 times reduction. In conclusion, we show that incorrect answers carry distinct and useful measurement information rather than representing equivalent mistakes.
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.