Ensemble forecasts often outperform forecasts from individual standalone models, and have been used to support decision-making and policy planning in various fields. As collaborative forecasting efforts to create effective ensembles grow, so does interest in understanding individual models' relative importance in the ensemble. To this end, we propose two practical methods that measure the difference between ensemble performance when a given model is or is not included in the ensemble: a leave-one-model-out algorithm and a leave-all-subsets-of-models-out algorithm, which is based on the Shapley value. We explore the relationship between these metrics, forecast accuracy, and the similarity of errors, both analytically and through simulations. We illustrate this measure of the value a component model adds to an ensemble in the presence of other models using US COVID-19 death probabilistic forecasts. This study offers valuable insight into individual models' unique features within an ensemble, which standard accuracy metrics alone cannot reveal.

翻译：集成预测通常优于单个独立模型的预测，并已在多个领域用于支持决策和政策规划。随着为创建有效集成而进行的协作预测工作的增加，理解个体模型在集成中的相对重要性也日益受到关注。为此，我们提出了两种实用的方法来衡量给定模型是否包含在集成中时集成性能的差异：一种是留一模型法，另一种是基于沙普利值的留所有模型子集法。我们通过分析和模拟，探讨了这些度量指标、预测准确度以及误差相似性之间的关系。我们利用美国COVID-19死亡概率预测，说明了在存在其他模型的情况下，一个组件模型为集成所增加的价值。这项研究为理解个体模型在集成中的独特特征提供了宝贵的见解，这是仅靠标准准确度指标无法揭示的。