Calibration is a pivotal aspect in predictive modeling, as it ensures that the predictions closely correspond with what we observe empirically. The contemporary calibration framework, however, is predominantly focused on prediction models where the outcome is a binary variable. We extend the logistic calibration framework to the generalized calibration framework which includes all members of the exponential family of distributions. We propose two different methods to estimate the calibration curve in this setting, a generalized linear model and a non-parametric smoother. In addition, we define two measures that summarize the calibration performance. The generalized calibration slope which quantifies the amount of over- or underfitting and the generalized calibration slope or calibration-in-the-large that measures the agreement between the global empirical average and the average predicted value. We provide an illustrative example using a simulated data set and hereby show how we can utilize the generalized calibration framework to assess the calibration of different types of prediction models.

翻译：校准是预测建模中的关键环节，它确保预测结果与实证观测高度一致。然而，当前的校准框架主要聚焦于结果为二元变量的预测模型。我们将逻辑斯蒂校准框架扩展为通用校准框架，该框架涵盖了指数族分布的所有成员。针对该设定下的校准曲线估计，我们提出了两种不同方法：广义线性模型和非参数平滑器。此外，我们定义了两种衡量校准性能的指标：通用校准斜率，用于量化过拟合或欠拟合的程度；以及通用校准斜率（即全局校准），用于衡量全局经验平均值与平均预测值之间的一致性。我们利用一个模拟数据集提供了示例说明，展示了如何运用通用校准框架评估不同类型预测模型的校准性能。