In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference for the cluster specific predictors is more intricate. This work introduces a general framework for multiple inference in linear mixed models for cluster specific predictors. Consistent simultaneous confidence sets for cluster specific predictors are constructed. Furthermore, it is shown that, while these simultaneous conditional confidence sets are feasible, remarkably, corresponding marginal confidence sets are also asymptotically valid for conditional inference. Those lend themselves for testing linear hypotheses using standard quantiles without the need of re-sampling techniques. All findings are validated in simulations and illustrated along a study on Spanish income data.

翻译：尽管对线性混合模型预测器具有高度的实际相关性,但迄今尚未讨论对线性混合模型预测器的多组具体推断,虽然对人口参数的边际推论是完全理解的,但对集型特定预测器的有条件推论则更为复杂。这项工作为集型特定预测器的线性混合模型引入了多重推论总框架。为集型特定预测器的线性混合模型构建了一致的同步信任套套件。此外,还表明,虽然这些同时的有条件信任套件是可行的,但明显的是,对应的边际信任套件对有条件推论也同样站不住脚。这些套件可以使用标准的量来测试线性假设,而不需要再抽样技术。所有结论都是在模拟中验证的,并在西班牙收入数据研究中加以说明。