Robustness for multilevel models: Fraud detection with the forward search

Several methods using multiple regression or classification tools are commonly adopted to identify outliers which are, perhaps, the most important statistical units for anti-fraud detection. For data in the European Union, which are here analysed, the presence of clusters of several firms and several countries, may hide structures and information, making standard and classical tools often unreliable. Moreover, even the parameters estimation of classical models can be severely biased by influential observations or outliers. A methodological solution is to exploit the natural hierarchical structure of multilevel models to take into account th time-varying evolution of quantities traded, and their price, for each country. Multilevel models, however, are not robust as they simply generalize linear models and ANOVA. A forward search algorithm is presented to make parameter estimation robust in the presence of outliers and avoiding masking and swamping, leading to a more accurate identification of suspicious firms. The influence of outliers, if any is inside the dataset, will be monitored at each step of the sequential procedure, which is the key element of the forward search. 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. An application to real data is also illustrated.