Are Multilevel functional models the next step in sports biomechanics and wearable technology? A case study of Knee Biomechanics patterns in typical training sessions of recreational runners

This paper illustrates how multilevel functional models can detect and characterize biomechanical changes along different sport training sessions. Our analysis focuses on the relevant cases to identify differences in knee biomechanics in recreational runners during low and high-intensity exercise sessions with the same energy expenditure by recording $20$ steps. To do so, we review the existing literature of multilevel models, and then, we propose a new hypothesis test to look at the changes between different levels of the multilevel model as low and high-intensity training sessions. We also evaluate the reliability of measures recorded in three-dimension knee angles from the functional intra-class correlation coefficient (ICC) obtained from the decomposition performed with the multilevel funcional model taking into account $20$ measures recorded in each test. The results show that there are no statistically significant differences between the two modes of exercise. However, we have to be careful with the conclusions since, as we have shown, human gait-patterns are very individual and heterogeneous between groups of athletes, and other alternatives to the p-value may be more appropriate to detect statistical differences in biomechanical changes in this context.