Checking identifiability of covariance parameters in linear mixed effects models

ABSTRACT

To build a linear mixed effects model, one needs to specify the random effects and often the associated parametrized covariance matrix structure. Inappropriate specification of the structures can result in the covariance parameters of the model not identifiable. Non-identifiability can result in extraordinary wide confidence intervals, and unreliable parameter inference. Sometimes software produces implication of model non-identifiability, but not always. In the simulation of fitting non-identifiable models we tried, about half of the times the software output did not look abnormal. We derive necessary and sufficient conditions of covariance parameters identifiability which does not require any prior model fitting. The results are easy to implement and are applicable to commonly used covariance matrix structures.

KEYWORDS:

• Covariance matrix structures
• identifiability
• mixed effects models
• random effects
• variance components

AMS SUBJECT CLASSIFICATION:

• 15A03
• 15A18
• 15B05
• 62J99

Acknowledgments

The author would like to thank the anonymous referees for very helpful comments that have improved presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.