The timing of events in birds’ annual cycles is important to understanding life history evolution and response to global climate change. Molt timing is often measured as an index of the sum of grown feather proportion or mass within the primary flight feathers. The distribution of these molt data over time has proven difficult to model with standard linear models. The parameters of interest are at change points in model fit over time, and so least-squares regression models that assume molt is linear violate the assumption of even variance. This has led to the introduction of other nonparametric models to estimate molt parameters. Hinge models directly estimate changes in model fit and have been used in many systems to find change points in data distributions. Here, we apply a hinge model to molt timing, through the introduction of a double-hinge (DH) threshold model. We then examine its performance in comparison to current models using simulated and empirical data. Our results suggest that the Underhill–Zucchini (UZ) and Pimm models perform well under many circumstances and appear to outperform the DH model in datasets with high variance. The DH model outperforms the UZ model at low sample sizes of birds in active molt and shorter molt durations and provides more realistic confidence intervals at smaller sample sizes. The DH model provides a novel addition to the toolkit for estimating molt phenology, expanding the conditions under which molt can accurately be estimated.

中文翻译：

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阈值模型改进了小样本数据集中蜕皮参数的估计

鸟类年度周期中事件的时间安排对于了解生命史演变和对全球气候变化的反应非常重要。蜕皮时间通常以初级飞羽中长出的羽毛比例或质量之和的指数来衡量。这些蜕皮数据随时间的分布已证明难以用标准线性模型建模。感兴趣的参数随着时间的推移处于模型拟合的变化点，因此假设蜕皮是线性的最小二乘回归模型违反了均匀方差的假设。这导致引入了其他非参数模型来估计蜕皮参数。铰链模型直接估计模型拟合的变化，并已在许多系统中用于查找数据分布中的变化点。在这里，我们将铰链模型应用于蜕皮时间，通过引入双铰链 (DH) 阈值模型。然后，我们使用模拟和经验数据检查其与当前模型相比的性能。我们的结果表明，Underhill-Zucchini (UZ) 和 Pimm 模型在许多情况下表现良好，并且在具有高方差的数据集中似乎优于 DH 模型。DH 模型在活跃蜕皮和较短蜕皮持续时间的鸟类样本量较小时优于 UZ 模型，并在较小样本量下提供更真实的置信区间。DH 模型为估计蜕皮物候的工具包提供了新的补充，扩大了准确估计蜕皮的条件。我们的结果表明，Underhill-Zucchini (UZ) 和 Pimm 模型在许多情况下表现良好，并且在具有高方差的数据集中似乎优于 DH 模型。DH 模型在活跃蜕皮和较短蜕皮持续时间的鸟类样本量较小时优于 UZ 模型，并在较小样本量下提供更真实的置信区间。DH 模型为估计蜕皮物候的工具包提供了新的补充，扩大了准确估计蜕皮的条件。我们的结果表明，Underhill-Zucchini (UZ) 和 Pimm 模型在许多情况下表现良好，并且在具有高方差的数据集中似乎优于 DH 模型。DH 模型在活跃蜕皮和较短蜕皮持续时间的鸟类样本量较小时优于 UZ 模型，并在较小样本量下提供更真实的置信区间。DH 模型为估计蜕皮物候的工具包提供了新的补充，扩大了准确估计蜕皮的条件。