Partially Ordered Sets: Partial Order Scalogram Analysis with Base Coordinates (POSAC)

Partial order scalogram analysis with base coordinates (POSAC) is a dimensionality reduction technique based on an iterative procedure that projects a set of m-dimensional partially ordered elements on a two-dimensional space, while preserving “as well as possible” their partial ordering relations. POSAC is part of the theory of Partially Ordered Sets and Facet theory, and it is mainly used in evaluation studies seeking a ranking or a prioritization of statistical units using a noncompensatory approach. Being a dimensionality reduction technique, POSAC implies a loss of information that is compensated by an easier interpretation of partial ordering in two rather than in m-dimensions. This makes POSAC especially useful to discuss policy strategies in front of nontechnical decision-makers.