Data from: On the use of double quantile regression and visual assessment to estimate performance constraints

<b>Abstract</b><br/><p>Quantile regression (QR) is a widely used tool for estimating performance limits in behavioral data. In <em>Vazquez-Cardona et al.</em> (2023, <em>Behavioral Ecology</em>), we applied mixed QR to estimate motor constraints in Adelaide’s warbler song, and measured performance as deviations from these estimated limits. A recent critique (Cardoso, 2024, <em>Behavioral Ecology</em>) raised two concerns about that analysis: (1) QR-based deviation scores arbitrarily emphasize one of the two variables in the trade-off, and (2) uneven sampling may produce the illusion of constraint, compromising the validity of visual assessments and QR. Here, we evaluate these claims by applying double quantile regression (DQR)—Cardoso’s proposed remedy—and by testing whether rarefaction alters the observed constraints. We introduce a novel method to characterize DQR results using bisecting lines and show that, for some distributions, DQR improves fit to the constrained edge. However, DQR performs poorly under some conditions and can falsely identify constraints in unconstrained data. Rarefaction analyses reveal that uneven sampling does not account for the appearance of constraint in our bird song data, which show sharp, bounded edges unlike the smooth gradients of unconstrained simulations. Finally, we demonstrate that the warm-up effect in vocal performance, previously reported in <em>Vazquez-Cardona et al.</em> (2023), is robust to both DQR-based estimation and rarefaction. We conclude that while DQR can be a useful complement to QR, visual inspection remains essential, and caution is warranted when applying DQR to datasets with complex geometries or potential false boundaries.</p>