Abstract When using univariate models, goodness of fit can be assessed through many different methods, including graphical tools such as half-normal plots with a simulation envelope. This is straightforward due to the notion of ordering of a univariate sample, which can readily reveal possible outliers. In the bivariate case, however, it is often difficult to detect extreme points and verify whether a sample of residuals is a reasonable realization from a fitted model. We propose a new framework, implemented as the bivrp R package, available on CRAN. Our framework uses the same principles of the simulation envelope in a half-normal plot, but as a simulation polygon for each point in a bivariate sample. By using algorithms of convex hull construction and polygon area reduction, we describe how our method works and illustrate its functionality with examples using simulated bivariate normal data and real bivariate count data. We show how different model diagnostics can produce different results and pinpoint potential drawbacks of our approach, such as the limitations in terms of computational burden. Supplementary materials for this article are available online.

中文翻译：

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带有模拟多边形的双变量残差图

摘要 当使用单变量模型时，拟合优度可以通过许多不同的方法进行评估，包括图形工具，例如带有模拟包络的半正态图。由于单变量样本的排序概念，这很简单，可以很容易地揭示可能的异常值。然而，在双变量情况下，通常很难检测极值点并验证残差样本是否是拟合模型的合理实现。我们提出了一个新框架，作为 bivrp R 包实现，可在 CRAN 上使用。我们的框架在半正态图中使用了与模拟包络相同的原理，但作为双变量样本中每个点的模拟多边形。通过使用凸包构造和多边形面积缩减算法，我们描述了我们的方法是如何工作的，并通过使用模拟双变量正态数据和真实双变量计数数据的示例来说明其功能。我们展示了不同的模型诊断如何产生不同的结果并指出我们方法的潜在缺点，例如计算负担方面的限制。本文的补充材料可在线获取。