Characterizing the functional ANOVA model for repeated measures via PCA application to biomechanical data

Gait analysis is a branch of biomechanics where its purpose is the study of mechanical laws relating to the way the body moves from one place to another. In most cases, the data sets for human gait analysis consist of continuous recordings of multiple physical activities, including kinematics and muscle performance. Despite the registered data being functions, the most common practice to detect any anomalies among experimental conditions consists of analyzing the vector of discrete observations or even summary measures of the curves. This fact causes an important information loss since the continuous nature of the data is being ignored. A suitable solution is to apply functional data analysis for analyzing continuous biomechanical data as functions, revealing the true nature of movement and allowing us to model and forecast the data with more precision. In the current paper, a new functional methodology for the analysis of variance with repeated measures was introduced. In particular, since functional data variability can be summarized by their first principal component scores, we proposed to turn the functional model into a multivariate one for the response of the most explicative principal components, and then, considered a semi-parametric approach to overcome the restrictive assumptions required in the classic repeated measures design. The motivation of this research was to contrast the differences in gait patterns of elementary school students when walking to school, depending on the type of bag they use to carry their school materials. The analysis reveals that gait joint movement is influenced by sex and the type of schoolbag, regardless of the load carried.