Data from: Optimizing phylogenetic eigenvector regression: Union eigenvectors, robust estimation, and flexible application to comparative analyses

Phylogenetic eigenvector regression (PVR) is widely used in ecology and
evolution by representing phylogenetic structure through separable
eigenvectors. Despite this flexibility, its implementation faces three key
challenges: (1) the selection of eigenvectors, (2) the reduced robustness
of ordinary least-squares (OLS) regression under shift-like evolutionary
heterogeneity, and (3) the applicability of conventional model complexity
rules such as the "samples-per-variable (SPV) ≥ 10" guideline.
Here, we propose an optimized PVR framework that addresses these
limitations. First, we show that trait-specific selections of eigenvectors
often diverge, sometimes producing inconsistent results, and that using
their union offers stronger control of phylogenetic non-independence.
Second, we evaluate robust regression estimators within PVR, demonstrating
that PVR-MM – and in most cases PVR-L2, the standard OLS estimator –
maintains high accuracy under non-stationary evolutionary shifts where
other non-robust methods fail. Third, through simulation, we reassess the
SPV ≥ 10 rule, showing that PVR tolerates eigenvector counts well beyond
this threshold, offering greater flexibility while requiring attention to
potential overfitting. Extensive simulations across diverse trees and
evolutionary scenarios confirm that the optimized framework improves
accuracy and robustness. By addressing key aspects of eigenvector
selection, regression, and model complexity, our findings strengthen the
reliability and applicability of PVR.