SEMbeddings: how to evaluate model misfit before data collection using large-language models

Introduction: Recent developments suggest that Large Language Models (LLMs) provide a promising approach for approximating empirical correlation matrices of item responses by utilizing item embeddings and their cosine similarities. In this paper, we introduce a novel tool, which we label SEMbeddings. Methods: This tool integrates mpnet-personality (a fine-tuned embedding model) with latent measurement models to assess model fit or misfit prior to data collection. To support our statement, we apply SEMbeddings to the 96 items of the VIA-IS-P, which measures 24 different character strengths, using responses from 31,697 participants. Results: Our analysis shows a significant, though not perfect, correlation (r = 0.67) between the cosine similarities of embeddings and empirical correlations among items. We then demonstrate how to fit confirmatory factor analyses on the cosine similarity matrices produced by mpnet-personality and interpret the outcomes using modification indices. We found that relying on traditional fit indices when using SEMbeddings can be misleading as they often lead to more conservative conclusions compared to empirical results. Nevertheless, they provide valuable suggestions about possible misfit, and we argue that the modification indices obtained from these models could serve as a useful screening tool to make informed decisions about items prior to data collection. Discussion: As LLMs become increasingly precise and new fine-tuned models are released, these procedures have the potential to deliver more reliable results, potentially transforming the way new questionnaires are developed.