Quantile regression for longitudinal within-race running data: the 2022 New York City Marathon

Abstract

Statistical methodology for complex data has significantly evolved over the past years to accommodate data types encountered in real life applications. For longitudinal data in particular, a large proportion of this adapted methodology focuses on traditional mean regression. Only in recent years some attention has gone to longitudinal quantile regression; moreover, mainly in a theoretical setting. The present article aims to bridge this gap by applying recent, copula-based longitudinal quantile regression methodology to data of the 2022 New York City Marathon, featuring intermediate time recordings. Previously, despite the ubiquity of such longitudinal race data in increasingly popular running events, they were typically reduced to one-dimensional data or used for ANOVA analyses only. The versatility of quantiles is furthermore illustrated by the introduction of three different types of quantile (or quantile-associated) curves, that are considered for several metrics quantifying runners' speed and pacing behaviour. The benefits are twofold: the potential of the methodology in this as well as similar contexts is illustrated, and the resulting, novel insights in runners' racing behaviour can assist athletes, coaches and experts in sports sciences.