Establishing Construct Validity in LLM Capability Benchmarks Requires Nomological Networks

The LLM community often reports benchmark results as if they are synonymous with general model capabilities. However, benchmarks can have problems that distort performance, like test set contamination and annotator error. How can we know that a benchmark is a reliable indicator of some capability that we want to measure? This question concerns the construct validity of LLM benchmarks, and it requires separating benchmark results from capabilities when we model and predict LLM performance. Both social scientists and computer scientists propose formal models - latent factor models and scaling laws - for identifying the capabilities underlying benchmark scores. However, neither technique is satisfactory for construct validity. Latent factor models ignore scaling laws, and as a result, the capabilities they extract often proxy model size. Scaling laws ignore measurement error, and as a result, the capabilities they extract are both uninterpretable and overfit to the observed benchmarks. This thesis presents the structured capabilities model, the first model to extract interpretable and generalisable capabilities from a large collection of LLM benchmark results. I fit this model and its two alternatives on a large sample of results from the OpenLLM Leaderboard. Structured capabilities outperform latent factor models on parsimonious fit indices, and exhibit better out-of-distribution benchmark prediction than scaling laws. These improvements are possible because neither existing approach separates model scale from capabilities in the appropriate way. Model scale should inform capabilities, as in scaling laws, and these capabilities should inform observed results up to measurement error, as in latent factor models. In combining these two insights, structured capabilities demonstrate better explanatory and predictive power for quantifying construct validity in LLM evaluations.

Despite remarkable progress on reasoning benchmarks, current LLM evaluation practice remains anchored to final-answer correctness, providing limited insight into how models reason, how reliably they behave under contextual variation, or how efficiently they reach conclusions. This paper proposes a unified multi-dimensional framework for measuring LLM reasoning quality from a behavioral perspective, operationalizing six theoretically grounded dimensions rooted in cognitive science: Correctness (CQ), Consistency (CS), Robustness (RS), Local Logical Coherence (LS), Efficiency (ES), and Stability (SS). The framework introduces deployment-aware aggregation, enabling context-specific model selection beyond accuracy-based leaderboards. Experiments across multiple LLMs and benchmarks reveal behaviors systematically concealed by single-metric evaluation, including the orthogonality of local logical coherence and correctness, deployment-context-dependent ranking inversions, and non-trivial dimensional profiles in small locally-deployed models. Discriminant validity analysis confirms that the proposed dimensions capture largely non-redundant signals. The resulting pipeline provides a foundation for diagnosing LLM reasoning behavior across deployment contexts, with domain-specific validation as a direction for future work.

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.