From Text to Parameters: Predicting Item Parameters from Embedding Regularization with Reliability and Design Ceilings
Authors: Shi-Ting Chen, Jinsong Chen
Organizations: Faculty of Education, The University of Hong Kong
Abstract
Newly developed items must ordinarily be field tested before their psychometric properties are known, creating a cold start problem for item calibration. Predicting item parameters from features is a long standing measurement problem dating back to the Linear Logistic Test Model; modern text embeddings now automate the design matrices traditionally specified by hand. We propose an evaluation framework combining regularized regression on item text embeddings, repeated cross validated R squared reported with its resampling standard deviation, and two performance upper bounds: a reliability ceiling derived from parameter standard errors, and a design ceiling derived from simulation based power calibration. Applying this framework to a mathematics item bank (EEDI) and a medical licensure benchmark (BEA 2024), we find that item difficulty is highly predictable from text (repeated cross validated R squared = 0.53, or about 57% of its reliability ceiling), whereas discrimination and pseudo guessing appear less predictable. However, evaluating these results against our ceilings reveals that this apparent hierarchy stems from target reliability rather than text signal strength: text uniformly recovers 57 to 63% of the reliable variance across difficulty targets, whereas the 3PL pseudo guessing parameter has a reliability ceiling near zero, making it an unviable target at current precision. On BEA, embedding based regression matches leaderboard RMSE despite explaining almost no variance, highlighting the critical need for scale free metrics and explicit ceilings in benchmarking. Finally, we show that a single train and test split can inflate apparent accuracy by 0.1 to 0.15 in R squared, underscoring the necessity of repeated cross validation for calibration support applications and future benchmark construction.
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.
Predicting item difficulty from content can provide an initial estimate for newly developed questions before sufficient student responses are available. Existing approaches typically represent the question stem and answer choices as text. When mathematics items contain visual components, a common pipeline first textualizes that evidence and then applies a text predictor. We ask: how should visual evidence be represented for item difficulty prediction? We compare question text alone, visual textualization, which expresses visual evidence in language, and image-native modeling, which retains the original image. Using Eedi items with difficulty calibrated from student responses, we train large language models (LLMs) and vision-language models (VLMs) directly for difficulty regression. Both visual interfaces achieve the lowest point estimates, although the leading systems cannot be reliably ordered. Open-VLM textualization yields lower RMSE point estimates for all evaluated LLMs, while broader adaptation does so for all image-native VLMs. Test-time interventions show dependence on the paired full-item image, but do not isolate the additional visual component. The two visual interfaces also make partially complementary item-level errors and differ substantially in computational workflow. Thus, textualization should not be treated as the only practical interface: image-native modeling is a competitive alternative whose effectiveness depends on how the VLM is adapted.
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.