The rapid development and growing deployment of large language models (LLMs) have made it increasingly important to understand their capabilities. A common approach is to evaluate LLMs using assessment instruments originally designed to measure skills and competencies in humans, such as standardized exams, and to use performance on these instruments as evidence for generalizable claims about LLMs' underlying abilities on the same skills the assessments are intended to measure in humans. However, from a validity perspective, such inferences require that the relationship between observed performance and underlying constructs established for humans also holds for LLMs. In particular, a necessary condition for transferring score interpretations is similarity in the latent structure of responses to the assessment. In this study, we examine whether this condition holds in two educational contexts: high-school chemistry and a quantitative reasoning section of a university entrance exam. Using a case study design, we compare human response data with responses generated by six multimodal LLMs. Our analytical approach combines exploratory factor analysis, factor congruence, and resampling to assess latent structure similarity across human learners and LLMs. Across both instruments, we find systematic differences between human and LLM factor structures, showing evidence that the analyzed assessments may not measure the same constructs for humans and LLMs. These findings call into question the validity of evaluation practices that use educational assessments to make claims about AI capabilities.
Figures & tables
Figure 1: Human vs. LLM EFA Structures Across Instruments. Factor retention based on Kaiser criterion.
Instrument
Kaiser Criterion
Parallel Analysis
Humans
LLMs
Humans
LLMs
Chemistry
4
4
5: 100%
4: 62.4% , 3: 16%, 5: 16%, 2: 5.2%, 7: 0.4%
Quantitative Reasoning
5
5
8: 66% , 7: 34%
5: 100%
Table 1: Factor-retention results for the Chemistry and Quantitative Reasoning instruments under the Kaiser criterion and parallel analysis. In the parallel analysis, the percentages refer to the proportion of runs that yielded each result.
Inst.
k
L-H sim.
H-H sim.
Cohen’s d
W
Quant.
4
0.438
0.543
1.80∗∗∗
8987.0
5
0.432
0.533
1.93∗∗∗
9060.5
7
0.456
0.531
1.67∗∗∗
8930.5
8
0.470
0.531
1.39∗∗∗
8370.0
Chem.
4
0.476
0.620
2.14∗∗∗
9441.5
5
0.500
0.587
1.45∗∗∗
8499.0
Table 2: Mean matched factor congruence scores across instruments and factor choices. H denotes human and L denotes LLMs, and Cohen’s d denotes the standardized difference between the two distributions. Statistical significance is denoted by ∗∗∗ , for p<.001 .
Figure 2: Distribution of mean matched factor congruence scores . Computed with Hungarian algorithm, for Human-Human and LLM-Human across datasets and Kaiser factor choice, on 100 resampled repetitions.
The evaluation of large language models (LLMs) relies heavily on human-designed assessments, implicitly assuming that AI and humans employ similar underlying cognitive constructs. Challenging this assumption, we investigate whether the latent factors governing LLM performance carry the same substantive, human-interpretable meaning as the cognitive constructs governing human learners. Using responses from humans and six LLMs across quantitative reasoning and chemistry assessments, we conducted Exploratory Factor Analysis (EFA) separately for both groups. Subject-Matter Experts (SMEs) then blindly evaluated the resulting factor graphs to ascribe pedagogical meaning to the emerged constructs. SMEs successfully interpreted most of the human-derived factors. Conversely, they could not ascribe meaning to any LLM-derived factors in quantitative reasoning and interpreted only half of the LLM factors in chemistry. By combining data-driven EFA with blind expert interpretation, this framework shows that LLMs frequently operate on statistically opaque mechanisms distinct from human reasoning.
The rapid adoption of large language models (LLMs) in education raises profound challenges for assessment design. To adapt assessments to the presence of LLM-based tools, it is crucial to characterize the strengths and weaknesses of LLMs in a generalizable, valid and reliable manner. However, current LLM evaluations often rely on descriptive statistics derived from benchmarks, and little research applies theory-grounded measurement methods to characterize LLM capabilities relative to human learners in ways that directly support assessment design. Here, by combining educational data mining and psychometric theory, we introduce a statistically principled approach for identifying items on which humans and LLMs show systematic response differences, pinpointing where assessments may be most vulnerable to AI misuse, and which task dimensions make problems particularly easy or difficult for generative AI. The method is based on Differential Item Functioning (DIF) analysis -- traditionally used to detect bias across demographic groups -- together with negative control analysis and item-total correlation discrimination analysis. It is evaluated on responses from human learners and six leading chatbots (ChatGPT-4o & 5.2, Gemini 1.5 & 3 Pro, Claude 3.5 & 4.5 Sonnet) to two instruments: a high school chemistry diagnostic test and a university entrance exam. Subject-matter experts then analyzed DIF-flagged items to characterize task dimensions associated with chatbot over- or under-performance. Results show that DIF-informed analytics provide a robust framework for understanding where LLM and human capabilities diverge, and highlight their value for improving the design of valid, reliable, and fair assessment in the AI era.
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.