A recap on Linear Mixed Models and their hat-matrices

This working paper has a twofold goal. On one hand, it provides a recap of Linear Mixed Models (LMMs): far from trying to be exhaustive, this rst part of the working paper focusses on the derivation of theoretical results on estimation of LMMs that are scattered in the literature or whose mathematical derivation is sometimes missing or too quickly sketched. On the other hand, it discusses various denitions that are available in the literature for the hat-matrix of Linear Mixed Models, showing their limitations and proving their equivalence