TY  - JOUR
A1  - Schöley, Jonas
T1  - The centered ternary balance scheme: A technique to visualize surfaces of unbalanced three-part compositions
Y1  - 2021/03/09
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 443
EP  - 458
DO  - 10.4054/DemRes.2021.44.19
VL  - S29
IS  - 19
UR  - https://www.demographic-research.org/special/29/19/
L1  - https://www.demographic-research.org/special/29/19/s29-19.pdf
L2  - https://www.demographic-research.org/special/29/19/s29-19.pdf
N2  - Background: The ternary balance scheme is a visualization technique that encodes three-part compositions as a mixture of three primary colors. The technique works best if the compositional data are well spread out across the domain but fails to show structure in very unbalanced data. 

Objective: I extend the ternary balance scheme such that it can be utilized to show variation in unbalanced compositional surfaces. 

Methods: By reprojecting an unbalanced compositional data set around its center of location and visualizing the transformed data with a standard ternary balance scheme, the internal variation of the data becomes visible. An appropriate centering operation has been defined within the field of compositional data analysis. 

Results: Using Europe’s regional workforce structure by economic sector as an example, I have demonstrated the utility of the centered ternary balance scheme in visualizing variation across unbalanced compositional surfaces. 

Contribution: I have proposed a technique to visualize the internal variation in surfaces of highly unbalanced compositional data and implemented it in the tricolore R package. 

ER  -