Partial order investigation of multiple indicator systems using variance-based sensitivity analysis

Partial order tools can be used in multiple criteria analysis to prioritize and rank a set of objects. In this setting the starting point is generally a matrix Mnxk of k observed indicators on n objects. Given that indicators are measured at least at the ordinal level, from matrix M its corresponding partially ordered set - poset - is set up to form the basis of multi-criteria ranking. The partial order may be very complex even when the number of objects to be compared is relatively small. The reason of such complexity is often due to the intrinsic nature of partial order which is exclusively based on the ordinal properties of the data matrix. Incomparabilities between objects can be due even to very small differences in the observed values of indicators thus causing ‘irrelevant’ incomparabilities. Also, objects may have been characterized with a redundant set of variables so that the change in the values of some indicators should not seriously affect the structure of the poset. These two opposite conditions are directly linked to the indicator level of influence and call for an indicator value related sensitivity analysis for testing the robustness of posets. In this work we propose a method to carry out a sensitivity analysis for posets by using variance-based sensitivity indices to detect main effects and interactions between indicators. To this aim, we characterize the poset structure with scalar measures and compute variance-based sensitivity indices according to the most recent practice for a fully exploratory sensitivity analysis. These indices allow for detecting least and most influencing indicators.