Data analyses by partial order methodology
Abstract
The present paper reviews data analysis applying partial order methodology. Hence, in addition to a short introduction to the basics of partial ordering a series of central tools of partial order methodology is presented and discussed based on exemplary studies applying a dataset comprising 12 obsolete pesticides characterized by their environmental persistence, bioaccumulation and toxicity.
Partial orders are often visualized by the so-called Hasse diagrams where the characteristics of partial ordering immediately become evident through the structure of the diagrams by levels, chains and antichains. Especially the presence of incomparabilities due to conflicting indicator values calls for attention.
The paper presents tools to a) estimate the relative importance of the single indicators applied, b) disclose the presence of so-called ‘peculiar’ objects that have one or more unexpected high or low indicator values, c) calculate the average order of the single element as partial ordering a priori does not lead to an absolute ordering that often is wanted, d) apply various weighting regimes in order to qualify the ordering, and e) disclose and visualize the actual nature of the incomparabilities that are in inherent part of partial ordering.
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