Ricerc@Sapienza

In composite indicators construction the robustness analysis is an important step suitable to validate the synthetic measure and to attempt to evaluate the loss of information.
This paper presents an interval between the best and the worst performance obtainable from the synthesis of a multi-indicator system, useful for the robustness analysis of composite indicators. The upper bound of this interval is obtained by using the Benefit Of The Doubt (BoD) approach and the lower bound is equal to the minimum between the basic indicators considered. The obtained range includes almost all synthetic measures that can be calculated with aggregative methods and it is suitable to analyze the distance of different values obtained by means of different methods from the best and the worst obtainable ones.

The mean value between the extremes of the interval is proposed as a new aggregation method. This medium point (MP) presents some interesting properties. It can be considered as only partially affected by compensability; in fact, it is exactly in the middle between the extreme calculated with the BoD, that is partially affected by compensation, and the minimum, that is totally non-compensative. Moreover, this point is the center of a symmetrical interval and, consequently, it gives an easily observable representation of the distance from the best and worst value obtainable from synthesis.

At the end, we propose a method to verify how properly a chosen synthetic method represents the structure of the data used by using model based clustering via finite Gaussian mixture models.
Assuming that the model based cluster analysis performed gives the best possible representation of the distribution of the data and assessing that every synthetic measure could be seen as an ordinal variable, we can evaluate the ordinal synthetic measure according to the miss-classification that it gives of the discriminatory capacity of the model based clustering.