Parameter Choice, Stability and Validity for Robust Cluster Weighted Modeling

Statistical inference based on the cluster weighted model often requires some subjective judgment from the modeler. Many features influence the final solution, such as the number of mixture components, the shape of the clusters in the explanatory variables, and the degree of heteroscedasticity of the errors around the regression lines. Moreover, to deal with outliers and contamination that may appear in the data, hyper-parameter values ensuring robust estimation are also needed. In principle, this freedom gives rise to a variety of “legitimate” solutions, each derived by a specific set of choices and their implications in modeling. Here we introduce a method for identifying a “set of good models” to cluster a dataset, considering the whole panorama of choices. In this way, we enable the practitioner, or the scientist who needs to cluster the data, to make an educated choice. They will be able to identify the most appropriate solutions for the purposes of their own analysis, in light of their stability and validity.

Robust Mahalanobis Distance based TOPSIS to Evaluate the Economic Development of Provinces

In this paper, 81 Turkish provinces with different development levels were ranked using the TOPSIS method. To evaluate the ranking with TOPSIS, we presented an improvement to Mahalanobis distances, by considering a robust MM estimator of the covariance matrix to deal with the presence of outliers in the dataset. Additionally, the homogenous subsets, which were obtained from the robust Mahalanobis distance-based TOPSIS were compared with robust cluster analysis. According to our findings, robust TOPSIS-M scores reflect the inter-class differences in economic developments of provinces spanning from the extremely low to the extremely high level of economic developments. Considering indicators of economic development, which are often used in the literature, İstanbul ranked first, Ankara second, and İzmir third according to the Robust TOPSIS-M method. Moreover, with the Robust Cluster analysis, these provinces were diagnosed as outliers and it was seen that obtained clusters were compatible with the ranking of Robust TOPSIS-M.