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

The authors are to be congratulated for an interesting paper which highlights the need for more formal procedures on the assessment of goodness of fit in the area of mixed models. The authors give a comprehensive overview of diagnostic techniques and goodness-of-fit tests for random effects in mixed models and propose a number of new nonparametric tests with omnibus character. Some of them are extensions of goodness-of-fit methods in the area of linear (regression) models and consequently share various properties of those. The paper addresses lack of fit tests for the distribution of the random effects and for the error distribution in a mixed model. The importance of this topic is vast. The application area of mixed models is broad—from longitudinal data to smoothing—and correct distributional assumptions are crucial for inference (see, e.g., Verbeke and Lesaffre 1997). Also, for the generalized linear mixed models, a misspecified distribution of random effects can lead to the substantial loss of efficiency (see, e.g., Agresti et al. 2004). We would like to address three issues in the following: