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Title: Isotemporal substitution in time-use behavioural data with compositional scalar-on-function regression Authors:  Paulina Jaskova - Palacky University Olomouc (Czech Republic) [presenting]
Karel Hron - Palacky University (Czech Republic)
Abstract: There is a relationship between the proportion of time spent in physical activity (PA) and health. The intensity of PA can be described through an increasing gravitational acceleration of movement. The question is how the relative reallocation of time between PA of various intensities is associated with the health, that is how to find an adequate regression model between the real response and covariate containing the time-use distribution. The time-use relative data 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 of PDFs to the $L_2$ space, a standard functional regression model with real response can be used. To describe the effect of certain subintervals 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. PA variables were modelled as continuous functional outcomes with the percentage body fat mass used as a health indicator. The results 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.