A0777
Title: A Bayesian semiparametric scalar on function regression with measurement error using instrumental variables
Authors: Roger Zoh - Indiana University (United States) [presenting]
Abstract: Wearable devices like the ActiGraph are increasingly used in research to track physical activity, reflecting the need to accurately assess the links between physical activity and health outcomes such as obesity. When evaluating the relationship between device-based physical activity measures and scalar outcomes like body mass index (BMI), these measures should be treated as functions. Scalar-on-function regression (SoFR) is an appropriate model in this context, but many estimation methods assume that measurement errors in functional covariates are white noise assumptions that, if violated, can lead to parameter underestimation. Current approaches for addressing measurement errors are limited to frequentist methods, and there are no solutions for Bayesian frameworks. A non-parametric Bayesian SoFR model is introduced that corrects measurement errors while relaxing traditional model assumptions. The method utilizes an instrumental variable that accommodates a time-varying bias and allows for model-based grouping of the functional covariate, enhancing the interpretability of the results. This approach is straightforward to implement, and extensive simulations demonstrate its finite sample properties. Finally, this method is applied to data from the National Health and Nutrition Examination Survey to evaluate the association between physical activity measured by wearables and BMI in U.S. adults.
