We describe a new residual for general regression models defined as , where y is the observed outcome and is a random variable from the fitted distribution. This probability‐scale residual (PSR) can be written as , whereas the popular observed‐minus‐expected residual can be thought of as . Therefore the PSR is useful in settings where differences are not meaningful or where the expectation of the fitted distribution cannot be calculated. We present several desirable properties of the PSR that make it useful for diagnostics and measuring residual correlation, especially across different outcome types. We demonstrate its utility for continuous, ordered discrete, and censored outcomes, including current status data, and with various models including Cox regression, quantile regression, and ordinal cumulative probability models, for which fully specified distributions are not desirable or needed, and in some cases suitable residuals are not available. The residual is illustrated with simulated data and real data sets from HIV‐infected patients on therapy in the southeastern United States and Latin America. The Canadian Journal of Statistics 44: 463–479; 2016 © 2016 Statistical Society of Canada

中文翻译：

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连续，离散和审查数据的概率标度残差。

我们描述了定义为的一般回归模型的新残差，其中y是观察到的结果，并且是来自拟合分布的随机变量。此概率规模残差（PSR）可以写成，而流行的观察到的负期望残差可以看成是。因此，PSR在差异无意义或无法计算拟合分布的期望的设置中很有用。我们介绍了PSR的几种理想特性，使其可用于诊断和测量残差相关性，尤其是在不同结果类型之间。我们展示了其在连续，有序离散和审查结果（包括当前状态数据）以及各种模型（包括Cox回归，分位数回归和有序累积概率模型）中的效用，在某些情况下不希望或不需要完全指定的分布在没有合适的残差的情况下。残余物用来自美国东南部和拉丁美洲接受HIV治疗的患者的模拟数据和真实数据集进行说明。《加拿大统计杂志》 44：463–479；2016©2016加拿大统计学会