In linear mixed-effects models, several frequentist and Bayesian measures have been proposed to evaluate model adequacy or/and to perform model selection. First, a large set of these measures are selected, presented with comparable notations, discussed in their strengths, weaknesses, and applicability range, and finally commented upon regarding their limitations. Then, these measures are illustrated on the home radon levels data (Gelman & Pardoe, Technometrics, 241-251, 48, 2006). Next, an extensive simulation study is carried out, to evaluate their sensitivity in selecting the correct model from a series of simpler models containing fewer parameters. Finally, recommendations on the use of these different measures are provided.