Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.
Keywords: National Health and Nutrition Examination Survey (NHANES); functional data analysis; horseshoe prior; pseudo-likelihood; pólya-Gamma.
© 2022 The International Biometric Society.