Compositional functional regression with isotemporal substitution and its application to time-use behavioural data

Speakers: Paulína Jašková  PhD-student

Palacký University Olomouc

Olomouc, Czech Republic

Abstract:  

There is a relationship between the proportion of time spent in physical activity (PA) and health. With the higher relative contribution of high-intensity PA on the total PA, a better health condition is expected and vice versa. Besides a simplification of a human activity profile into a few intensity categories, it can be described on a continuous scale through an increasing gravitational acceleration of movement. The question remains on how the relative reallocation of the proportion of time between PA of various intensities is associated with the health. In other words, there is a need for an adequate regression model between the real response and covariate containing the time-use distribution.

The time-use relative data, referred to as compositional data with parts corresponding to PA categories which form covariates in the usual compositional reallocation models, can be extended to the continuous case as probability density functions (PDFs). Similar to compositional data, PDFs are also characterized by the scale invariance property and are geometrically represented using the so-called Bayes spaces. After a proper transformation which maps PDFs from the Bayes space to the L2 space, a standard functional regression model with real response can be used. To describe the effect of certain subintervals (subdomains) of the gravitational acceleration PDF, an isotemporal substitution can be used for amplifying the impact of particular levels of PA on the health outcome.

The presented method was applied to a dataset consisting of functional observations resulting from a large study conducted among school-aged children from the Czech Republic. In this case, the analytic sample consists of 74 girls between the ages of 14 and 17 years. PA variables (independent variable) were assessed using tri-axial accelerometers and modelled as continuous functional outcomes based on the Euclidean Norm Minus One metric. The percentage body fat mass was used as a health indicator (dependent variable). The results of the regression analysis with added isotemporal substitution confirm the natural expectation as the more time is spent in the PA of higher intensity is associated with a lower percentage of fat mass.