Comments on: Goodness-of-fit-tests in mixed models

Abstract

I am very pleased to have the opportunity to discuss this interesting paper. The authors deal with the problem of assessing normality of random effects and/or error distributions in the context of mixed models. As clearly stated in Sect. 1 of the manuscript, this is not only a question of theoretical importance, but it has practical implications as well. In Sects. 3 and 4 of the manuscript there is a very exhaustive overview of available methods. There are essentially two kinds of procedures, graphical methods, which are of no inferential nature, that try to mimic the use of normal probability plots in the context of regression but take into account that the residuals of the mixed model are correlated. Another alternative is the use of classical tests, such as Shapiro Wilk, after trying to “independize” the residuals. A test specifically designed for checking normality in mixed models is that of Jiang (2001), where a χ2 type of tests is proposed, and some power studies are made. These results are compared with the ones proposed in Sect. 6 of the paper, and we present here a related simulation study. The authors address the problem in a very particular fashion. They rather estimate the density of the random effects (and the error terms when needed) instead of the actual effects, and propose two frameworks: order selection/smooth tests and minimum distance estimators. As for the order selection methods, the authors base their proposal on a smooth test based on (truncated) expansions of ( fU(u)