论文标题
回归模型中诊断图的全局模拟信封
Global simulation envelopes for diagnostic plots in regression models
论文作者
论文摘要
剩余图通常用于审问回归模型假设，但是解释它们需要了解在满足假设时会期望多少样本变化。在本文中，我们建议在剩余图上构建围绕数据的全球信封（或围绕数据趋势），从而利用了最近的进步，从而可以通过模拟围绕函数构建全球信封。尽管提出的工具主要是作为图形辅助工具，但它们可以解释为模型假设的正式测试，该测试可以通过仿真实验研究其性质。我们考虑了三个模型场景 - 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量式图的数据构建的全局仿真包络测试的功能，或者围绕残留与拟合图的趋势线或规模地点图的趋势线。在检测违反分布和线性假设的情况下，将全球包膜测试与常用的假设测试进行了比较。免费可用的\ texttt {r}软件（\ texttt {ecostats :: plotenvelope}）可以将这些工具应用于具有具有\ texttt {simulate}的方法的任何拟合模型，\ texttttt {nortsuals}和\ texttt {precedit} {preceje predict}函数。
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.
