New Techniques and Technologies for Statistics (NTTS) 2017
17 March 2017
Multi-indicator systems and partially ordered sets
- Filomena Maggino (University of Rome “La Sapienza” – Italy)
- Marco Fattore (university of Milan-Bicocca – Italy)
The full programme available in the .PDF file linked to at the top of this page; please also refer to the online version.
Developing indicators describing a reality which is complex produces a complex system. This characteristic may require approaches allowing more concise views able to summarizing the complexity. In this perspective, the guiding concept crossing all possible strategies is synthesis.
However, a synthetic indicator obtained through the aggregative approach is hardly able to reflect the complexity of a socio-economic phenomenon and capture the complexity of the relationships between variables.
The way out to this impasse can be found in realizing that synthesis does not necessarily imply aggregation. In other words, non-aggregative approaches are needed, able to (i) respect the ordinal nature of the data and the process and trends of phenomena (not always linear but more frequently monotonic), (ii) avoid any aggregation among indicators, and (iii) producing a synthetic indicator.
In this perspective, one of the most useful references is the Partial Order Theory, a branch of discrete mathematics providing concepts and tools that fit very naturally the needs of ordinal data analysis. Tools referring to that theory, in particular Partially Ordered Set (POSET), allow for the extraction of information directly out of the relational structure of the data. The conclusions drawn through the application of POSET methodologies are much more meaningful, robust and consistent than those based upon traditional statistical tools.