Marginal and Conditional Multiple Inference in Linear Mixed Models
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This work introduces a general framework for multiple inference in linear mixed models. Inference in mixed models can be done about population effects (marginal) and about subject specific characteristics (conditional). For two asymptotic scenarios that adequately address settings arising in practice, we construct consistent simultaneous confidence sets for subject specific characteristics. We show that remarkably marginal confidence sets are still asymptotically valid for conditional inference. The resulting sets are suitable for multiple testing and thus fill a gap in the literature that is of practical relevance. We confirm our findings with a simulation study and real data example of Spanish income data.
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