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

• Published in: Sociological methods & research Vol. 54; no. 3; pp. 1074 - 1109
• Main Authors: Broska, David, Howes, Michael, van Loon, Austin
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.08.2025; SAGE PUBLICATIONS, INC
• Subjects: Behavior; Cost analysis; Cost Effectiveness; Human subjects; Humans; Inequality; Large language models; Power structure; Predictions; Productivity; Research subjects; prediction-powered inference (PPI); PPI correlation; mixed subjects design; effective sample size; large language models; PPI poweranalysis; machine learning; computational social science
• ISSN: 0049-1241; 1552-8294
• DOI: 10.1177/00491241251326865

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.