Robustness for multilevel models with the forward search

Robustness of standard regression models have been studied quite extensively. When repeated measures are available, the methodological framework is generalized to multilevel models, for which little is known in term of robustness, even in the simplest case of ANOVA. We present a sequential forward search algorithm for multilevel models that allows robust and efficient parameters estimation in presence of outliers, and it avoids masking and swamping. The influence of outliers will be monitored at each step of the sequential procedure, which is the key element of the forward search. There are peculiar features when the forward search is applied to multilevel models. Such features pose new computational challenges, as some restrictions, that make the sub-models identifiable at every step, are required. The method is illustrated by an application to real data where exports of coffee to European countries are modeled and analyzed to identify outliers that might be linked to potential frauds. Preliminary results on simulated data have highlighted the benefit of adopting the forward search algorithm, which can reveal masked outliers, influential observations and show hidden structures.