Aligning LLM-Simulated and Human Examinees for Psychometric Calibration: A Cognitive Diagnostic Profiling Approach

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.

Psychological instruments designed for humans are increasingly used to assign large language models (LLMs) stable psychological profiles that affect their usability, safety assessment, and use as proxies for human participants in research. Using a formal psychometric framework, we show that these profiles are largely a measurement artifact. Administering a battery of personality and risk-preference instruments spanning self-reports and behavioral tasks to 56 instruction-tuned LLMs alongside large human reference samples, we report four findings. First, differences between models are driven not by the traits an instrument targets but by a directional response bias, a tendency to respond toward one end of the scale, or one labeled option, regardless of item content; a variance decomposition attributes 81-90% of between-model variation to this bias, against 9-16% in humans. Second, the bias declines with model capability but is not eliminated by it. Third, because bias rather than trait drives responding, an instrument's apparent reliability is almost entirely predicted by its response orthogonality, a term we coin for the proportion of items for which trait and bias point in opposite directions. Fourth, the profile a model appears to have shifts with the items used and can be manufactured through item selection. These results demonstrate that the apparent psychological profiles of LLMs are artifacts of the instrument used to measure them, not properties of the models themselves. As instruments borrowed from human psychology are rarely fully orthogonal and may inherently lack validity for LLMs, we call for dedicated assessments centered on response orthogonality.

The Metacognitive Probe is an exploratory five-task, 15-slot diagnostic that decomposes an LLM's confidence behaviour into five behaviourally-distinct dimensions: confidence calibration (T1-CC), epistemic vigilance (T2-EV), knowledge boundary (T3-KB), calibration range (T4-CR), and reasoning-chain validation (T5-RCV). It is evaluated on N=8 frontier models and N=69 humans. The instrument is motivated by Flavell (1979) and Nelson and Narens (1990) but operates on observable confidence-correctness alignment; it is not a validated cross-species metacognition scale, and the pre-specified human developmental hypothesis was falsified. Composite benchmarks (MMLU, BIG-Bench, HELM, GPQA) ask whether a model produces a correct response. They are silent on whether the model knows when its response is wrong. A model can score 80 on a composite calibration benchmark and still be wildly overconfident in narrow pockets the aggregate cannot surface. The Metacognitive Probe surfaces those pockets. Our headline is a 47-point within-model dissociation in Gemini 2.5 Flash: panel-best within-task calibration (T1-CC = 88; Spearman rho = +0.551, 95% CI [+0.14, +0.80], p = 0.005) and panel-worst cross-task difficulty prediction (T4-CR = 41; sigma_conf = 1.4 across twelve factoids).