  Object-oriented data analysis is a fascinating and developing field in modern
statistical science with the potential to make significant and valuable
contributions to biomedical applications. This statistical framework allows for
the formalization of new methods to analyze complex data objects that capture
more information than traditional clinical biomarkers. The paper applies the
object-oriented framework to analyzing and predicting physical activity
measured by accelerometers. As opposed to traditional summary metrics, we
utilize a recently proposed representation of physical activity data as a
distributional object, providing a more sophisticated and complete profile of
individual energetic expenditure in all ranges of monitoring intensity. For the
purpose of predicting these distributional objects, we propose a novel hybrid
Frechet regression model and apply it to US population accelerometer data from
NHANES 2011-2014. The semi-parametric character of the new model allows us to
introduce non-linear effects for essential variables, such as age, that are
known from a biological point of view to have nuanced effects on physical
activity. At the same time, the inclusion of a global for linear term retains
the advantage of interpretability for other variables, particularly categorical
covariates such as ethnicity and sex. The results obtained in our analysis are
helpful from a public health perspective and may lead to new strategies for
optimizing physical activity interventions in specific American subpopulations.
