Robust random effects models: a diagnostic approach based on the forward search

This paper presents a robust procedure for the detection of atypical observations and for the analysis of their effect on model inference in random effects models. Given that the observations can be outlying at different levels of the analysis, we focus on the evaluation of the effect of both first and second level outliers and, in particular, on their effect on the higher level variance which is statistically evaluated with the Likelihood-Ratio Test. A cut-off point separating the outliers from the other observations is identified through a graphical analysis of the information collected at each step of the Forward Search procedure; the Robust Forward LRT is the value of the classical LRT statistic at the cut-off point. © Springer-Verlag Berlin Heidelberg 2013.