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 are monitored at each step of the sequential procedure. There are peculiar features when the forward search is applied to multilevel models which pose new computational challenges, as the sub- models must be identifiable at every step. Preliminary results on simulated data highlight the benefit of adopting the forward search algorithm, which can reveal masked influential observations.
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