Robust Approaches for Fuzzy Clusterwise Regression Based on Trimming and Constraints

Three different approaches for robust fuzzy clusterwise regression are reviewed. They are all based on the simultaneous application of trimming and constraints. The first one follows from the joint modeling of the response and explanatory variables through a normal component fitted in each cluster. The second one assumes normally distributed error terms conditional on the explanatory variables while the third approach is an extension of the Cluster Weighted Model. A fixed proportion of “most outlying” observations are trimmed. The use of appropriate constraints turns these problem into mathematically well-defined ones and, additionally, serves to avoid the detection of non-interesting or “spurious” linear clusters. The third proposal is specially appealing because it is able to protect us against outliers in the explanatory variables which may act as “bad leverage” points. Feasible and practical algorithms are outlined. Their performances, in terms of robustness, are illustrated in some simple simulated examples.