  A multiplicative effects model is introduced for the identification of the
factors that are influential to the performance of highly-trained endurance
runners. The model extends the established power-law relationship between
performance times and distances by taking into account the effect of the
physiological status of the runners, and training effects extracted from GPS
records collected over the course of a year. In order to incorporate
information on the runners' training into the model, the concept of the
training distribution profile is introduced and its ability to capture the
characteristics of the training session is discussed. The covariates that are
relevant to runner performance as response are identified using a procedure
termed multi-resolution elastic net. Multi-resolution elastic net allows the
simultaneous identification of scalar covariates and of intervals on the domain
of one or more functional covariates that are most influential for the
response. The results identify a contiguous group of speed intervals between
5.3 to 5.7 m$\cdot$s$^{-1}$ as influential for the improvement of running
performance and extend established relationships between physiological status
and runner performance. Another outcome of multi-resolution elastic net is a
predictive equation for performance based on the minimization of the mean
squared prediction error on a test data set across resolutions.
