The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross‐validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial‐, the t‐, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia.

中文翻译：

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混合模型的条件协方差惩罚

混合模型的预测误差可以根据研究重点而有条件或有边际。我们为混合模型引入了乐观定理的新型条件版本，该模型将条件预测误差与混合模型的协方差惩罚联系起来。引入了用于估计这些条件协方差惩罚的不同可能性。这些是引导方法，交叉验证和称为Steinian的直接方法。在模拟研究中，针对二项式，t和γ分布以及不同种类的预测误差，评估了不同估算技术的行为。此外，基于赞比亚营养不良的应用，讨论了估计技术对预测误差的影响。