Probability-scale residuals for continuous, discrete, and censored data.
Probability-scale residuals for continuous, discrete, and censored data.
复制标题
DOI：
10.1002/cjs.11302
复制
发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
Liu Q
中科院分区：
文献类型：
--
作者：
Shepherd BE;Li C;Liu Q
我们描述了一般回归模型的一种新的残差，定义为Pr(Y*<；y)−Pr(Y*>；y)，其中y是观测结果，Y*是来自拟合分布的随机变量。这种概率尺度残差可以写成E{−(y，Y*)}，而流行的观测减去预期残差可以认为是E(y Sign Y*)。因此，在差异没有意义或无法计算拟合分布的期望值的情况下，概率尺度残差是有用的。我们提出了概率尺度残差的几个理想性质，这使得它对于诊断和测量残差相关性是有用的，特别是在不同的结果类型之间。我们展示了它对连续的、有序的离散的和删失的结果的有效性，包括当前的状态数据，以及各种模型，包括Cox回归、分位数回归和顺序累积概率模型，对于这些模型，完全指定的分布是不理想的或不需要的，在某些情况下，合适的残差是不可用的。剩余部分用模拟数据和来自美国东南部和拉丁美洲艾滋病毒感染患者治疗的真实数据集进行了说明。
We describe a new residual for general regression models, defined as pr(Y* < y) − pr(Y* > y), where y is the observed outcome and Y* is a random variable from the fitted distribution. This probability-scale residual can be written as E {sign(y, Y*)} whereas the popular observed-minus-expected residual can be thought of as E(y − Y*). Therefore, the probability-scale residual 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 probability-scale residual 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 datasets from HIV-infected patients on therapy in the southeastern United States and Latin America.