Overcoming the problem of multicollinearity in sports performance data: A novel application of partial least squares...

Professional sporting organisations invest considerable resources collecting and analysing data in order to better understand the factors that influence performance. Recent advances in non-invasive technologies, such as global positioning systems (GPS), mean that large volumes of data are now readily available to coaches and sport scientists. However analysing such data can be challenging, particularly when sample sizes are small and data sets contain multiple highly correlated variables, as is often the case in a sporting context. Multicollinearity in particular, if not treated appropriately, can be problematic and might lead to erroneous conclusions. In this paper we present a novel 'leave one variable out' (LOVO) partial least squares correlation analysis (PLSCA) methodology, designed to overcome the problem of multicollinearity, and show how this can be used to identify the training load (TL) variables that influence most 'end fitness' in young rugby league players.

The accumulated TL of sixteen male professional youth rugby league players (17.7 ± 0.9 years) was quantified via GPS, a micro-electrical-mechanical-system (MEMS), and players' session-rating-of-perceived-exertion (sRPE) over a 6-week pre-season training period. Immediately prior to and following this training period, participants undertook a 30-15 intermittent fitness test (30-15IFT), which was used to determine a players 'starting fitness' and 'end fitness'. In total twelve TL variables were collected, and these along with 'starting fitness' as a covariate were regressed against 'end fitness'. However, considerable multicollinearity in the data (VIF >1000 for nine variables) meant that the multiple linear regression (MLR) process was unstable and so we developed a novel LOVO PLSCA adaptation to quantify the relative importance of the predictor variables and thus minimise multicollinearity issues. As such, the LOVO PLSCA was used as a tool to inform and refine the MLR process.

The LOVO PLSCA identified the distance accumulated at very-high speed (>7 m·s-1) as being the most important TL variable to influence improvement in player fitness, with this variable causing the largest decrease in singular value inertia (5.93). When included in a refined linear regression model, this variable, along with 'starting fitness' as a covariate, explained 73% of the variance in v30-15IFT 'end fitness' (p<0.001) and eliminated completely any multicollinearity issues.

The LOVO PLSCA technique appears to be a useful tool for evaluating the relative importance of predictor variables in data sets that exhibit considerable multicollinearity. When used as a filtering tool, LOVO PLSCA produced a MLR model that demonstrated a significant relationship between 'end fitness' and the predictor variable 'accumulated distance at very-high speed' when 'starting fitness' was included as a covariate. As such, LOVO PLSCA may be a useful tool for sport scientists and coaches seeking to analyse data sets obtained using GPS and MEMS technologies.