AI benchmarks increasingly leverage item-level statistical models, particularly item response theory (IRT), to estimate model capabilities, rank systems, select informative examples, and diagnose benchmark quality. However, AI benchmark data often departs from the data regime of human testing, for which standard IRT estimation tools were originally developed: benchmarks typically involve fewer evaluated models, far more items, and capability distributions that may be skewed, clustered, or multimodal. We examine how these regime mismatches challenge the reliability of IRT modeling for AI evaluation. Using item parameters and capability distributions derived from six widely used LLM benchmarks, we simulate response matrices under three common IRT models and compare four estimation tools used in recent benchmark studies: marginal maximum likelihood, Markov chain Monte Carlo, variational inference, and a neural pseudo-Siamese estimator. Across 18,000 simulation conditions, we systematically evaluate computational feasibility, scalability, and the reliability of IRT inferences about model rankings, predicted performance, and item characteristics. Results show that classical estimators can become infeasible in large benchmark settings, whereas scalable estimators can produce unreliable item-level and ranking inferences with small or nonnormally distributed model sets. This study identifies when latent trait models reliably support or risk distorting AI benchmarking claims, and what sample sizes and diagnostics are needed for trustworthy use.
Retail intelligence often relies on monitoring popular, high-velocity products, potentially biasing economic indicators by ignoring the "long tail" of niche items. This simulation study investigates selection bias in inflation estimation and compares correction methods across diverse data-generating processes. Through 400 Monte Carlo replications spanning four scenarios--aligned step functions, smooth gradients, misaligned breaks, and polynomial relationships--we test the robustness of Inverse Probability Weighting (IPW) with five specifications against stratification with varying strata counts. Our findings reveal fundamental limits of weighting methods in retail long-tail contexts: stratification achieves superior performance in three of four scenarios, maintaining sub-0.04pp median error even when boundaries deliberately misalign with population breaks (116x advantage over IPW). However, IPW with spline propensity models wins under smooth polynomial relationships (median error 0.007pp vs. 0.013pp), demonstrating context-dependency. Critically, even an oracle IPW specification with perfect structural knowledge achieves 6.06pp error compared to stratification's 0.008pp in step-function scenarios. This reflects violation of the Positivity Assumption--a fundamental causal inference requirement--rather than IPW methodological inferiority. When selection probabilities differ dramatically (90% vs. 1%), weighting methods operate outside their theoretical design envelope. These results demonstrate that stratification provides a safer engineering choice in retail long-tail distributions with severe positivity violations.
Yawen Ma, Sahoko Ishida, Kate Cain +1cs.LG stat.AP
Digital learning environments record learners' responses to individual items, making it possible to study the development of specific skills rather than overall scores. Drawing conclusions about learning from these data requires a model that links responses to latent skills and tracks how mastery changes over time. When the skills measured by each item are unknown, the analyst must decide whether to estimate this structure, the Q-matrix, jointly with the learning process, or to establish it first and study learning afterwards. We show that this decision can change substantive conclusions about how learners develop. Using dynamic cognitive diagnostic models, we analyse data from two reading games measuring vocabulary and comprehension from Grade 2 to Grade 3, with item-text embeddings providing prior information for the unknown Q-matrix. A joint analysis and a bias-corrected stepwise analysis agree that most learners move toward mastering both skills, but disagree about how many remain only partially proficient at Grade 3, changing how reading progress would be reported. A simulation study identifies when the two analyses diverge and shows that joint analysis is more reliable when the item-skill structure is uncertain and the item pool changes between grades. We provide R code for both analyses.