The Mixed Subjects Design: Treating Large Language Models as Potentially Informative Observations

Abstract

Large Language Models (LLMs) provide cost-effective but possibly inaccurate predictions of human behavior. Despite growing evidence that predicted and observed behavior are often not interchangeable, there is limited guidance on using LLMs to obtain valid estimates of causal effects and other parameters. We argue that LLM predictions should be treated as potentially informative observations, while human subjects serve as a gold standard in a mixed subjects design. This paradigm preserves validity and offers more precise estimates at a lower cost than experiments relying exclusively on human subjects. We demonstrate-and extend-prediction-powered inference (PPI), a method that combines predictions and observations. We define the PPI correlation as a measure of interchangeability and derive the effective sample size for PPI. We also introduce a power analysis to optimally choose between informative but costly human subjects and less informative but cheap predictions of human behavior. Mixed subjects designs could enhance scientific productivity and reduce inequality in access to costly evidence.

Keywords: Mixed Subjects Design, Prediction-Powered Inference, PPI Correlation, Effective Sample Size, PPI Power Analysis, Machine Learning, Large Language Models, Computational Social Science