The t linear mixed model: model formulation, identifiability and estimation

The robustness of the t linear mixed model (tLMM) has been proved and exploited in many applications. Various publications emerged with the aim of proving superiority with respect to traditional linear mixed models, extending to more general settings and proposing more efficient estimation methods. However, little attention has been paid to the mathematical properties of the model itself and to the evaluation of the proposed estimation methods. In this paper we perform an in-depth analysis of the tLMM, evaluating a direct maximum likelihood estimation method via an intensive simulation study and investigating some identifiability properties. The theoretical findings are illustrated through an application to a dataset collected from a sleep trial.