Iterated multisource exchangeability models for individualized inference with an application to mobile sensor data

Researchers are increasingly interested in using sensor technology to collect accurate activity information and make individualized inference about treatments, exposures, and policies. How to optimally combine population data with data from an individual remains an open question. Multisource exchangeability models (MEMs) are a Bayesian approach for increasing precision by combining potentially heterogeneous supplemental data sources into analysis of a primary source. MEMs are a potentially powerful tool for individualized inference but can integrate only a few sources; their model space grows exponentially, making them intractable for high‐dimensional applications. We propose iterated MEMs (iMEMs), which identify a subset of the most exchangeable sources prior to fitting a MEM model. iMEM complexity scales linearly with the number of sources, and iMEMs greatly increase precision while maintaining desirable asymptotic and small sample properties. We apply iMEMs to individual‐level behavior and emotion data from a smartphone app and show that they achieve individualized inference with up to 99% efficiency gain relative to standard analyses that do not borrow information.