Functional Data Analysis of Head Impact Exposure of College Football Athletes
摘要
College football players often sustain impacts that might lead to concussion. Helmet-attached accelerometers track instantaneous head acceleration and are capable of detecting impacts. The dataset analyzed in the paper records longitudinally collected Head Acceleration Events (HAEs) from college football players playing at different positions and from several schools. We model the number of HAEs as count data and use functional data methods to quantify the varying patterns of HAEs in a season and evaluate how they might differ across positions and from school to school. In particular, we decompose a matrix of functions via the Tucker decomposition of tensors, which leads to an interpretable and stable model estimation of school and position-specific mean patterns of HAEs. For the proposed model, we develop an efficient model estimation algorithm that combines expectation-maximization (EM) and nonparametric function estimation via penalized splines. The proposed model, when applied to the HAEs dataset, gives sensible results. Simulation studies also demonstrate good performance of the proposed model estimation algorithm.