PATCH! {P}sychometrics-{A}ssis{T}ed Ben{CH}marking of Large Language Models against Human Populations: A Case Study of Proficiency in 8th Grade Mathematics

Many existing benchmarks of large (multimodal) language models (LLMs) focus on measuring LLMs' academic proficiency, often with also an interest in comparing model performance with human test takers'. While such benchmarks have proven key to the development of LLMs, they suffer from several limitations, including questionable measurement quality (e.g., Do they measure what they are supposed to in a reliable way?), lack of quality assessment on the item level (e.g., Are some items more important or difficult than others?) and unclear human population reference (e.g., To whom can the model be compared?). In response to these challenges, we propose leveraging knowledge from psychometrics -- a field dedicated to the measurement of latent variables like academic proficiency -- into LLM benchmarking. We make four primary contributions. First, we reflect on current LLM benchmark developments and contrast them with psychometrics-based test development. Second, we introduce PATCH: a novel framework for {P}sychometrics-{A}ssis{T}ed ben{CH}marking of LLMs. PATCH addresses the aforementioned limitations. In particular, PATCH enables valid comparison between LLMs and human populations. Third, we demonstrate PATCH by measuring several LLMs' proficiency in 8th grade mathematics against 56 human populations. We show that adopting a psychometrics-based approach yields evaluation outcomes that diverge from those based on current benchmarking practices. Fourth, we release 4 high-quality datasets to support measuring and comparing LLM proficiency in grade school mathematics and science with human populations.