On the CTA-PLS test for hierarchical models: an application to the football player’s performance

This study aims to develop and explore an inferential procedure for implementing the Confirmatory tetrad analysis (CTA-PLS) multiple test in a hierarchical Partial least squares structural equation model (PLS-SEM) framework for addressing theoretical constructs (reflective or formative); the approach is applied to evaluate the performance of football players. In the paper, the procedure for the second order (potentially extendable to higher orders) is proposed, then the results of a simulation to estimate the actual significance level and power are presented; finally, the multiple test aims to specify an original second-order hierarchical model, proposing an alternative for measuring goalkeepers performance. In the simulation, the Bonferroni and the Benjamini-Hochberg corrections are considered across diverse scenarios, and the results are that the Bonferroni correction tends to be overly conservative, exhibiting diminished power, particularly evident in smaller sample sizes. The sport application illustrates the efficacy of this approach in measuring goalkeeper performance within the world of football analytics, revealing some interesting and useful implications for football stakeholders.