Residual plots are often used to interrogate regression model assumptions, but interpreting them requires an understanding of how much sampling variation to expect when assumptions are satisfied. In this paper, we propose constructing global envelopes around data (or around trends fitted to data) on residual plots, exploiting recent advances that enable construction of global envelopes around functions by simulation. While the proposed tools are primarily intended as a graphical aid, they can be interpreted as formal tests of model assumptions, which enables the study of their properties via simulation experiments. We considered three model scenarios -- fitting a linear model, generalized linear model or generalized linear mixed model -- and explored the power of global simulation envelope tests constructed around data on quantile-quantile plots, or around trend lines on residual vs fits plots or scale-location plots. Global envelope tests compared favorably to commonly used tests of assumptions at detecting violations of distributional and linearity assumptions. Freely available \texttt{R} software (\texttt{ecostats::plotenvelope}) enables application of these tools to any fitted model that has methods for the \texttt{simulate}, \texttt{residuals} and \texttt{predict} functions.

中文翻译：

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回归模型中诊断图的全局模拟包络

残差图通常用于询问回归模型假设，但解释它们需要了解在满足假设时预期的抽样变化量。在本文中，我们建议在残差图上围绕数据（或围绕数据拟合的趋势）构建全局包络，利用最近的进展，通过模拟围绕函数构建全局包络。虽然建议的工具主要用作图形辅助，但它们可以解释为模型假设的正式测试，从而可以通过模拟实验研究它们的特性。我们考虑了三种模型场景——拟合线性模型、广义线性模型或广义线性混合模型——并探索了围绕分位数-分位数图上的数据构建的全局模拟包络测试的能力，或围绕残差与拟合图或比例位置图上的趋势线。在检测违反分布和线性假设的情况下，全局包络测试优于常用的假设测试。免费提供的 \texttt{R} 软件 (\texttt{ecostats::plotenvelope}) 可以将这些工具应用于任何具有 \texttt{simulate}、\texttt{residuals} 和 \texttt{predict} 函数的方法的拟合模型.