Visualizing Count Data Regressions Using Rootograms

The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here, we extend the rootogram to regression models and show that this is particularly useful for diagnosing and treating issues such as overdispersion and/or excess zeros in count data models. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, for example, in finite mixture models. An empirical illustration revisiting a well-known dataset from ethology is included, for which a negative binomial hurdle model is employed. Supplementary materials providing two further illustrations are available online: the first, using data from public health, employs a two-component finite mixture of negative binomial models; the second, using data from finance, involves underdispersion. An R implementation of our tools is available in the R package countreg. It also contains the data and replication code.

根图（rootogram）是与约翰·W·图基（J. W. Tukey）的研究相关的图形工具，最初用于评估单变量分布的拟合优度。本文将根图拓展至回归模型场景，并证明其在诊断和处理计数数据模型中的过度离散及/或过量零值等问题时尤为实用。我们还提出了根图的加权版本，可应用于样本外数据或数据的（加权）子集，例如在有限混合模型中。本文纳入了一项针对行为学领域经典数据集的实证重分析示例，该示例采用负二项障碍模型进行建模。在线补充材料提供了另外两项示例：其一基于公共卫生数据，采用两分量负二项模型有限混合结构；其二基于金融学数据，涉及欠离散问题。本文所提出工具的R语言实现已收录于R包countreg，该包同时包含相关数据集与复现代码。