Identifiability of linear mixed effects models

In mixed effects model, observations are a function of fixed and random effects and an error term. This structure determines a very specific structure for the variances and covariances of these observations. Unfortunately, the specific parameters of this variance/covariance structure might not be identifiable. Nonidentifiability can lead to complications in numerical estimation algorithms or worse, to incorrect or ambiguous inference. We study the identifiability of normal linear mixed effects models. We derive necessary and sufficient conditions of identifiability and we study identifiability in some commonly used variance-covariance structures. The results are particularly timely, given the recent interest in linear mixed effects models within the longitudinal and functional data analysis literature. With that in mind, we extend our discussion to identifiability in models for scalar responses depending on function-valued covariates.

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