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.
翻译:残留的图案通常用于询问回归模型假设,但解释这些图案时需要了解假设满足时有多少抽样差异。在本文中,我们提议围绕剩余图案的数据(或与数据相适应的趋势)构建全球信封,利用最近的进展,以便能够在模拟功能周围构建全球信封。虽然拟议的工具主要是为了图解辅助,但可以被解释为模型假设的正式测试,从而可以通过模拟实验研究其属性。我们考虑了三个模型情景 -- -- 适合线性模型、通用线性模型或普遍线性线性混合模型 -- -- 并探讨了围绕量性-量性图案数据或残余图案或规模定位图案趋势线条建立的全球模拟信封测试的威力。全球信封测试与通常使用的用于检测违反分配和线性假设情况的假设测试相比,是有利的。自由提供的\textt{R}软件(textt{ecoostats:plotenvelop})能够将这些工具应用到任何符合模型的模型,这些模型中具有tutt{sresuldule、{{\trest}}}和{trestrestrests}}}}}}{trestrestrestrets。