标题： 方法：在动物科学中使用广义可加模型 显示英文标题

标题： Method: Using generalized additive models in the animal sciences

摘要： 动物科学研究中经常遇到协变量与感兴趣响应变量之间的非线性关系。 在统计模型中，这些非线性效应传统上是通过一系列方法来处理的，包括对响应进行变换、基于理论或现象学基础的参数化非线性模型（例如，泌乳曲线），或者通过固定样条或多项式项。 如果希望直接从数据中学习关系的形状，广义可加模型（GAMs）是这些传统方法的一个优秀替代方案。 GAMs扩展了广义线性模型，使得线性预测器包含一个或多个平滑函数，这些函数使用惩罚样条进行参数化。 对每个函数施加一个波动性惩罚，以避免过度拟合，在估计样条基函数参数时最大化对数据的拟合度，同时不产生过于复杂的函数。 现代GAMs包括自动平滑选择方法，以找到估计函数拟合度和复杂度之间的最佳平衡。 由于GAMs从数据中学习函数的形状，用户可以避免将特定模型强加于自己的数据。 在这里，我提供GAMs的简要描述，并通过视觉方式说明它们的工作原理。 然后，我通过三个复杂度逐渐增加的示例数据集展示GAMs的实用性，以说明i）从数据中学习可以比参数化模型更好地拟合数据，ii）如何使用分层GAMs在一个模型中估计多个动物的生长数据，以及iii）如何使用分层GAMs在设计实验中进行正式的统计推断，以研究母体激素暴露对日本鹌鹑后续生长的影响。 显示英文摘要

摘要： Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of approaches, including transformation of the response, parametric nonlinear models based on theory or phenomenological grounds (e.g., lactation curves), or through fixed spline or polynomial terms. If it is desirable to learn the shape of the relationship from the data directly, then generalized additive models (GAMs) are an excellent alternative to these traditional approaches. GAMs extend the generalized linear model such that the linear predictor includes one or more smooth functions, parameterised using penalised splines. A wiggliness penalty on each function is used to avoid over fitting while estimating the parameters of the spline basis functions to maximise fit to the data without producing an overly complex function. Modern GAMs include automatic smoothness selection methods to find an optimal balance between fit and complexity of the estimated functions. Because GAMs learn the shapes of functions from the data, the user can avoid forcing a particular model to their data. Here, I provide a brief description of GAMs and visually illustrate how they work. I then demonstrate the utility of GAMs on three example data sets of increasing complexity, to show i) how learning from data can produce a better fit to data than that of parametric models, ii) how hierarchical GAMs can be used to estimate growth data from multiple animals in a single model, and iii) how hierarchical GAMs can be used for formal statistical inference in a designed experiment of the effects of exposure to maternal hormones on subsequent growth in Japanese quail.